abydos.distance package

abydos.distance.

The distance package implements string distance measure and metric classes:

These include traditional Levenshtein edit distance and related algorithms:

Hamming distance (Hamming), Relaxed Hamming distance (RelaxedHamming), and the closely related Modified Language-Independent Product Name Search distance (MLIPNS) are provided.

Block edit distances:

Distance metrics developed for the US Census or derived from them are included:

A large set of multi-set token-based distance metrics are provided, including:

Three popular sequence alignment algorithms are provided:

Classes relating to substring and subsequence distances include:

A number of simple distance classes provided in the package include:

Normalized compression distance classes for a variety of compression algorithms are provided:

Three similarity measures from SeatGeek's FuzzyWuzzy:

A convenience class, allowing one to pass a list of string transforms (phonetic algorithms, string transforms, and/or stemmers) and, optionally, a string distance measure to compute the similarity/distance of two strings that have undergone each transform, is provided in:

The remaining distance measures & metrics include:

Most of the distance and similarity measures have sim and dist methods, which return a measure that is normalized to the range \([0, 1]\). The normalized distance and similarity are always complements, so the normalized distance will always equal 1 - the similarity for a particular measure supplied with the same input. Some measures have an absolute distance method dist_abs that is not limited to any range.

All three methods can be demonstrated using the DamerauLevenshtein class:

>>> dl = DamerauLevenshtein()
>>> dl.dist_abs('orange', 'strange')
2
>>> dl.dist('orange', 'strange')
0.2857142857142857
>>> dl.sim('orange', 'strange')
0.7142857142857143

abydos.distance.sim(src, tar, method=<function sim_levenshtein>)[source]

Return a similarity of two strings.

This is a generalized function for calling other similarity functions.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • method (function) -- Specifies the similarity metric (sim_levenshtein() by default)

Returns

Similarity according to the specified function

Return type

float

Raises

AttributeError -- Unknown distance function

Examples

>>> round(sim('cat', 'hat'), 12)
0.666666666667
>>> round(sim('Niall', 'Neil'), 12)
0.4
>>> sim('aluminum', 'Catalan')
0.125
>>> sim('ATCG', 'TAGC')
0.25

New in version 0.1.0.

abydos.distance.dist(src, tar, method=<function sim_levenshtein>)[source]

Return a distance between two strings.

This is a generalized function for calling other distance functions.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • method (function) -- Specifies the similarity metric (sim_levenshtein() by default) -- Note that this takes a similarity metric function, not a distance metric function.

Returns

Distance according to the specified function

Return type

float

Raises

AttributeError -- Unknown distance function

Examples

>>> round(dist('cat', 'hat'), 12)
0.333333333333
>>> round(dist('Niall', 'Neil'), 12)
0.6
>>> dist('aluminum', 'Catalan')
0.875
>>> dist('ATCG', 'TAGC')
0.75

New in version 0.1.0.

class abydos.distance.Levenshtein(mode='lev', cost=(1, 1, 1, 1), normalizer=<built-in function max>, taper=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Levenshtein distance.

This is the standard edit distance measure. Cf. [Lev65][Lev66].

Optimal string alignment (aka restricted Damerau-Levenshtein distance) [Boy11] is also supported.

The ordinary Levenshtein & Optimal String Alignment distance both employ the Wagner-Fischer dynamic programming algorithm [WF74].

Levenshtein edit distance ordinarily has unit insertion, deletion, and substitution costs.

New in version 0.3.6.

Changed in version 0.4.0: Added taper option

Initialize Levenshtein instance.

Parameters
  • mode (str) --

    Specifies a mode for computing the Levenshtein distance:

    • lev (default) computes the ordinary Levenshtein distance, in which edits may include inserts, deletes, and substitutions

    • osa computes the Optimal String Alignment distance, in which edits may include inserts, deletes, substitutions, and transpositions but substrings may only be edited once

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • taper (bool) -- Enables cost tapering. Following [ZD96], it causes edits at the start of the string to "just [exceed] twice the minimum penalty for replacement or deletion at the end of the string".

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

alignment(src, tar)[source]

Return the Levenshtein alignment of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

A tuple containing the Levenshtein distance and the two strings, aligned.

Return type

tuple

Examples

>>> cmp = Levenshtein()
>>> cmp.alignment('cat', 'hat')
(1.0, 'cat', 'hat')
>>> cmp.alignment('Niall', 'Neil')
(3.0, 'N-iall', 'Nei-l-')
>>> cmp.alignment('aluminum', 'Catalan')
(7.0, '-aluminum', 'Catalan--')
>>> cmp.alignment('ATCG', 'TAGC')
(3.0, 'ATCG-', '-TAGC')
>>> cmp = Levenshtein(mode='osa')
>>> cmp.alignment('ATCG', 'TAGC')
(2.0, 'ATCG', 'TAGC')
>>> cmp.alignment('ACTG', 'TAGC')
(4.0, 'ACT-G-', '--TAGC')

New in version 0.4.1.

dist(src, tar)[source]

Return the normalized Levenshtein distance between two strings.

The Levenshtein distance is normalized by dividing the Levenshtein distance (calculated by either of the two supported methods) by the greater of the number of characters in src times the cost of a delete and the number of characters in tar times the cost of an insert. For the case in which all operations have \(cost = 1\), this is equivalent to the greater of the length of the two strings src & tar.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Levenshtein distance between src & tar

Return type

float

Examples

>>> cmp = Levenshtein()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.6
>>> cmp.dist('aluminum', 'Catalan')
0.875
>>> cmp.dist('ATCG', 'TAGC')
0.75

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the Levenshtein distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Levenshtein distance between src & tar

Return type

int (may return a float if cost has float values)

Examples

>>> cmp = Levenshtein()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
7
>>> cmp.dist_abs('ATCG', 'TAGC')
3
>>> cmp = Levenshtein(mode='osa')
>>> cmp.dist_abs('ATCG', 'TAGC')
2
>>> cmp.dist_abs('ACTG', 'TAGC')
4

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.levenshtein(src, tar, mode='lev', cost=(1, 1, 1, 1))[source]

Return the Levenshtein distance between two strings.

This is a wrapper of Levenshtein.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • mode (str) --

    Specifies a mode for computing the Levenshtein distance:

    • lev (default) computes the ordinary Levenshtein distance, in which edits may include inserts, deletes, and substitutions

    • osa computes the Optimal String Alignment distance, in which edits may include inserts, deletes, substitutions, and transpositions but substrings may only be edited once

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

Returns

The Levenshtein distance between src & tar

Return type

int (may return a float if cost has float values)

Examples

>>> levenshtein('cat', 'hat')
1
>>> levenshtein('Niall', 'Neil')
3
>>> levenshtein('aluminum', 'Catalan')
7
>>> levenshtein('ATCG', 'TAGC')
3
>>> levenshtein('ATCG', 'TAGC', mode='osa')
2
>>> levenshtein('ACTG', 'TAGC', mode='osa')
4

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Levenshtein.dist_abs method instead.

abydos.distance.dist_levenshtein(src, tar, mode='lev', cost=(1, 1, 1, 1))[source]

Return the normalized Levenshtein distance between two strings.

This is a wrapper of Levenshtein.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • mode (str) --

    Specifies a mode for computing the Levenshtein distance:

    • lev (default) computes the ordinary Levenshtein distance, in which edits may include inserts, deletes, and substitutions

    • osa computes the Optimal String Alignment distance, in which edits may include inserts, deletes, substitutions, and transpositions but substrings may only be edited once

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

Returns

The Levenshtein distance between src & tar

Return type

float

Examples

>>> round(dist_levenshtein('cat', 'hat'), 12)
0.333333333333
>>> round(dist_levenshtein('Niall', 'Neil'), 12)
0.6
>>> dist_levenshtein('aluminum', 'Catalan')
0.875
>>> dist_levenshtein('ATCG', 'TAGC')
0.75

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Levenshtein.dist method instead.

abydos.distance.sim_levenshtein(src, tar, mode='lev', cost=(1, 1, 1, 1))[source]

Return the Levenshtein similarity of two strings.

This is a wrapper of Levenshtein.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • mode (str) --

    Specifies a mode for computing the Levenshtein distance:

    • lev (default) computes the ordinary Levenshtein distance, in which edits may include inserts, deletes, and substitutions

    • osa computes the Optimal String Alignment distance, in which edits may include inserts, deletes, substitutions, and transpositions but substrings may only be edited once

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

Returns

The Levenshtein similarity between src & tar

Return type

float

Examples

>>> round(sim_levenshtein('cat', 'hat'), 12)
0.666666666667
>>> round(sim_levenshtein('Niall', 'Neil'), 12)
0.4
>>> sim_levenshtein('aluminum', 'Catalan')
0.125
>>> sim_levenshtein('ATCG', 'TAGC')
0.25

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Levenshtein.sim method instead.

class abydos.distance.DamerauLevenshtein(cost=(1, 1, 1, 1), normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Damerau-Levenshtein distance.

This computes the Damerau-Levenshtein distance [Dam64]. Damerau-Levenshtein code is based on Java code by Kevin L. Stern [Ste14], under the MIT license: https://github.com/KevinStern/software-and-algorithms/blob/master/src/main/java/blogspot/software_and_algorithms/stern_library/string/DamerauLevenshteinAlgorithm.java

Initialize Levenshtein instance.

Parameters
  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the Damerau-Levenshtein similarity of two strings.

Damerau-Levenshtein distance normalized to the interval [0, 1].

The Damerau-Levenshtein distance is normalized by dividing the Damerau-Levenshtein distance by the greater of the number of characters in src times the cost of a delete and the number of characters in tar times the cost of an insert. For the case in which all operations have \(cost = 1\), this is equivalent to the greater of the length of the two strings src & tar.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Damerau-Levenshtein distance

Return type

float

Examples

>>> cmp = DamerauLevenshtein()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.6
>>> cmp.dist('aluminum', 'Catalan')
0.875
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the Damerau-Levenshtein distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Damerau-Levenshtein distance between src & tar

Return type

int (may return a float if cost has float values)

Raises

ValueError -- Unsupported cost assignment; the cost of two transpositions must not be less than the cost of an insert plus a delete.

Examples

>>> cmp = DamerauLevenshtein()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
7
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.damerau_levenshtein(src, tar, cost=(1, 1, 1, 1))[source]

Return the Damerau-Levenshtein distance between two strings.

This is a wrapper of DamerauLevenshtein.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

Returns

The Damerau-Levenshtein distance between src & tar

Return type

int (may return a float if cost has float values)

Examples

>>> damerau_levenshtein('cat', 'hat')
1
>>> damerau_levenshtein('Niall', 'Neil')
3
>>> damerau_levenshtein('aluminum', 'Catalan')
7
>>> damerau_levenshtein('ATCG', 'TAGC')
2

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the DamerauLevenshtein.dist_abs method instead.

abydos.distance.dist_damerau(src, tar, cost=(1, 1, 1, 1))[source]

Return the Damerau-Levenshtein similarity of two strings.

This is a wrapper of DamerauLevenshtein.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

Returns

The normalized Damerau-Levenshtein distance

Return type

float

Examples

>>> round(dist_damerau('cat', 'hat'), 12)
0.333333333333
>>> round(dist_damerau('Niall', 'Neil'), 12)
0.6
>>> dist_damerau('aluminum', 'Catalan')
0.875
>>> dist_damerau('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the DamerauLevenshtein.dist method instead.

abydos.distance.sim_damerau(src, tar, cost=(1, 1, 1, 1))[source]

Return the Damerau-Levenshtein similarity of two strings.

This is a wrapper of DamerauLevenshtein.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 1))

Returns

The normalized Damerau-Levenshtein similarity

Return type

float

Examples

>>> round(sim_damerau('cat', 'hat'), 12)
0.666666666667
>>> round(sim_damerau('Niall', 'Neil'), 12)
0.4
>>> sim_damerau('aluminum', 'Catalan')
0.125
>>> sim_damerau('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the DamerauLevenshtein.sim method instead.

class abydos.distance.ShapiraStorerI(cost=(1, 1), prime=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Shapira & Storer I edit distance with block moves, greedy algorithm.

Shapira & Storer's greedy edit distance [SS07] is similar to Levenshtein edit distance, but with two important distinctions:

  • It considers blocks of characters, if they occur in both the source and target strings, so the edit distance between 'abcab' and 'abc' is only 1, since the substring 'ab' occurs in both and can be inserted as a block into 'abc'.

  • It allows three edit operations: insert, delete, and move (but not substitute). Thus the distance between 'abcde' and 'deabc' is only 1 because the block 'abc' can be moved in 1 move operation, rather than being deleted and inserted in 2 separate operations.

If prime is set to True at initialization, this employs the greedy' algorithm, which limits replacements of blocks in the two strings to matching occurrences of the LCS.

New in version 0.4.0.

Initialize ShapiraStorerI instance.

Parameters
  • prime (bool) -- If True, employs the greedy' algorithm rather than greedy

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Shapira & Storer I distance.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Shapira & Storer I distance between src & tar

Return type

float

Examples

>>> cmp = ShapiraStorerI()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.333333333333
>>> cmp.dist('aluminum', 'Catalan')
0.6
>>> cmp.dist('ATCG', 'TAGC')
0.25

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Shapira & Storer I edit distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Shapira & Storer I edit distance between src & tar

Return type

int

Examples

>>> cmp = ShapiraStorerI()
>>> cmp.dist_abs('cat', 'hat')
2
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
9
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.4.0.

class abydos.distance.Marking(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Ehrenfeucht & Haussler's marking distance.

This edit distance [EH88] is the number of marked characters in one word that must be masked in order for that word to consist entirely of substrings of another word.

It is normalized by the length of the first word.

New in version 0.4.0.

Initialize Marking instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized marking distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

marking distance

Return type

float

Examples

>>> cmp = Marking()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.6
>>> cmp.dist('aluminum', 'Catalan')
0.625
>>> cmp.dist('ATCG', 'TAGC')
0.5
>>> cmp.dist('cbaabdcb', 'abcba')
0.25

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the marking distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

marking distance

Return type

int

Examples

>>> cmp = Marking()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
5
>>> cmp.dist_abs('ATCG', 'TAGC')
2
>>> cmp.dist_abs('cbaabdcb', 'abcba')
2

New in version 0.4.0.

class abydos.distance.MarkingMetric(**kwargs)[source]

Bases: abydos.distance._marking.Marking

Ehrenfeucht & Haussler's marking metric.

This metric [EH88] is the base 2 logarithm of the product of the marking distances between each term plus 1 computed in both orders. For strings x and y, this is:

\[dist_{MarkingMetric}(x, y) = log_2((diff(x, y)+1)(diff(y, x)+1))\]

The function diff is Ehrenfeucht & Haussler's marking distance Marking.

New in version 0.4.0.

Initialize MarkingMetric instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized marking distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

marking distance

Return type

float

Examples

>>> cmp = Marking()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.6
>>> cmp.dist('aluminum', 'Catalan')
0.625
>>> cmp.dist('ATCG', 'TAGC')
0.5
>>> cmp.dist('cbaabdcb', 'abcba')
0.25

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the marking distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

marking distance

Return type

int

Examples

>>> cmp = MarkingMetric()
>>> cmp.dist_abs('cat', 'hat')
2.0
>>> cmp.dist_abs('Niall', 'Neil')
3.584962500721156
>>> cmp.dist_abs('aluminum', 'Catalan')
4.584962500721156
>>> cmp.dist_abs('ATCG', 'TAGC')
3.169925001442312
>>> cmp.dist_abs('cbaabdcb', 'abcba')
2.584962500721156

New in version 0.4.0.

class abydos.distance.YujianBo(cost=(1, 1, 1, 1), **kwargs)[source]

Bases: abydos.distance._levenshtein.Levenshtein

Yujian-Bo normalized Levenshtein distance.

Yujian-Bo's normalization of Levenshtein distance [YB07], given Levenshtein distance \(GLD(X, Y)\) between two strings X and Y, is

\[dist_{N-GLD}(X, Y) = \frac{2 \cdot GLD(X, Y)}{|X| + |Y| + GLD(X, Y)}\]

New in version 0.4.0.

Initialize YujianBo instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the Yujian-Bo normalized edit distance between strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Yujian-Bo normalized edit distance between src & tar

Return type

float

Examples

>>> cmp = YujianBo()
>>> round(cmp.dist('cat', 'hat'), 12)
0.285714285714
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.5
>>> cmp.dist('aluminum', 'Catalan')
0.6363636363636364
>>> cmp.dist('ATCG', 'TAGC')
0.5454545454545454

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Yujian-Bo normalized edit distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Yujian-Bo normalized edit distance between src & tar

Return type

int

Examples

>>> cmp = YujianBo()
>>> cmp.dist_abs('cat', 'hat')
0.2857142857142857
>>> cmp.dist_abs('Niall', 'Neil')
0.5
>>> cmp.dist_abs('aluminum', 'Catalan')
0.6363636363636364
>>> cmp.dist_abs('ATCG', 'TAGC')
0.5454545454545454

New in version 0.4.0.

class abydos.distance.HigueraMico(**kwargs)[source]

Bases: abydos.distance._distance._Distance

The Higuera-Micó contextual normalized edit distance.

This is presented in [delHigueraMico08].

This measure is not normalized to a particular range. Indeed, for an string of infinite length as and a string of 0 length, the contextual normalized edit distance would be infinity. But so long as the relative difference in string lengths is not too great, the distance will generally remain below 1.0

Notes

The "normalized" version of this distance, implemented in the dist method is merely the minimum of the distance and 1.0.

New in version 0.4.0.

Initialize Levenshtein instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the bounded Higuera-Micó distance between two strings.

This is the distance bounded to the range [0, 1].

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The bounded Higuera-Micó distance between src & tar

Return type

float

Examples

>>> cmp = HigueraMico()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.5333333333333333
>>> cmp.dist('aluminum', 'Catalan')
0.7916666666666667
>>> cmp.dist('ATCG', 'TAGC')
0.6000000000000001

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Higuera-Micó distance between two strings.

This is a straightforward implementation of Higuera & Micó pseudocode from [delHigueraMico08], ported to Numpy.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Higuera-Micó distance between src & tar

Return type

float

Examples

>>> cmp = HigueraMico()
>>> cmp.dist_abs('cat', 'hat')
0.3333333333333333
>>> cmp.dist_abs('Niall', 'Neil')
0.5333333333333333
>>> cmp.dist_abs('aluminum', 'Catalan')
0.7916666666666667
>>> cmp.dist_abs('ATCG', 'TAGC')
0.6000000000000001

New in version 0.4.0.

class abydos.distance.Indel(**kwargs)[source]

Bases: abydos.distance._levenshtein.Levenshtein

Indel distance.

This is equivalent to Levenshtein distance, when only inserts and deletes are possible.

New in version 0.3.6.

Initialize Levenshtein instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized indel distance between two strings.

This is equivalent to normalized Levenshtein distance, when only inserts and deletes are possible.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized indel distance

Return type

float

Examples

>>> cmp = Indel()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.333333333333
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.454545454545
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.3.6.

abydos.distance.indel(src, tar)[source]

Return the indel distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Indel distance

Return type

int

Examples

>>> indel('cat', 'hat')
2
>>> indel('Niall', 'Neil')
3
>>> indel('Colin', 'Cuilen')
5
>>> indel('ATCG', 'TAGC')
4

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Indel.dist_abs method instead.

abydos.distance.dist_indel(src, tar)[source]

Return the normalized indel distance between two strings.

This is equivalent to normalized Levenshtein distance, when only inserts and deletes are possible.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized indel distance

Return type

float

Examples

>>> round(dist_indel('cat', 'hat'), 12)
0.333333333333
>>> round(dist_indel('Niall', 'Neil'), 12)
0.333333333333
>>> round(dist_indel('Colin', 'Cuilen'), 12)
0.454545454545
>>> dist_indel('ATCG', 'TAGC')
0.5

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Indel.dist method instead.

abydos.distance.sim_indel(src, tar)[source]

Return the normalized indel similarity of two strings.

This is equivalent to normalized Levenshtein similarity, when only inserts and deletes are possible.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized indel similarity

Return type

float

Examples

>>> round(sim_indel('cat', 'hat'), 12)
0.666666666667
>>> round(sim_indel('Niall', 'Neil'), 12)
0.666666666667
>>> round(sim_indel('Colin', 'Cuilen'), 12)
0.545454545455
>>> sim_indel('ATCG', 'TAGC')
0.5

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Indel.sim method instead.

class abydos.distance.SAPS(cost=(1, -1, -4, 6, -2, -1, -3), normalizer=<built-in function max>, tokenizer=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Syllable Alignment Pattern Searching tokenizer.

This is the alignment and similarity calculation described on p. 917-918 of [RY05].

New in version 0.4.0.

Initialize SAPS instance.

Parameters
  • cost (tuple) --

    A 7-tuple representing the cost of the four possible matches:

    • syllable-internal match

    • syllable-internal mis-match

    • syllable-initial match or mismatch with syllable-internal

    • syllable-initial match

    • syllable-initial mis-match

    • syllable-internal gap

    • syllable-initial gap

    (by default: (1, -1, -4, 6, -2, -1, -3))

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized SAPS similarity between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized SAPS similarity between src & tar

Return type

float

Examples

>>> cmp = SAPS()
>>> round(cmp.sim('cat', 'hat'), 12)
0.0
>>> round(cmp.sim('Niall', 'Neil'), 12)
0.2
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the SAPS similarity between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The SAPS similarity between src & tar

Return type

int

Examples

>>> cmp = SAPS()
>>> cmp.sim_score('cat', 'hat')
0
>>> cmp.sim_score('Niall', 'Neil')
3
>>> cmp.sim_score('aluminum', 'Catalan')
-11
>>> cmp.sim_score('ATCG', 'TAGC')
-1
>>> cmp.sim_score('Stevenson', 'Stinson')
16

New in version 0.4.0.

class abydos.distance.MetaLevenshtein(tokenizer=None, corpus=None, metric=None, normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Meta-Levenshtein distance.

Meta-Levenshtein distance [MYCappe08] combines Soft-TFIDF with Levenshtein alignment.

New in version 0.4.0.

Initialize MetaLevenshtein instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • corpus (UnigramCorpus) -- A unigram corpus UnigramCorpus. If None, a corpus will be created from the two words when a similarity function is called.

  • metric (_Distance) -- A string distance measure class for making soft matches, by default Jaro-Winkler.

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Levenshtein distance between two strings.

The Levenshtein distance is normalized by dividing the Levenshtein distance (calculated by any of the three supported methods) by the greater of the number of characters in src times the cost of a delete and the number of characters in tar times the cost of an insert. For the case in which all operations have \(cost = 1\), this is equivalent to the greater of the length of the two strings src & tar.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Levenshtein distance between src & tar

Return type

float

Examples

>>> cmp = MetaLevenshtein()
>>> round(cmp.dist('cat', 'hat'), 12)
0.205186754296
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.507780131444
>>> cmp.dist('aluminum', 'Catalan')
0.8675933954313434
>>> cmp.dist('ATCG', 'TAGC')
0.8077801314441113

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the Meta-Levenshtein distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Meta-Levenshtein distance

Return type

float

Examples

>>> cmp = MetaLevenshtein()
>>> cmp.dist_abs('cat', 'hat')
0.6155602628882225
>>> cmp.dist_abs('Niall', 'Neil')
2.538900657220556
>>> cmp.dist_abs('aluminum', 'Catalan')
6.940747163450747
>>> cmp.dist_abs('ATCG', 'TAGC')
3.2311205257764453

New in version 0.4.0.

class abydos.distance.Covington(weights=(0, 5, 10, 30, 60, 100, 40, 50), **kwargs)[source]

Bases: abydos.distance._distance._Distance

Covington distance.

Covington distance [Cov96]

New in version 0.4.0.

Initialize Covington instance.

Parameters
  • weights (tuple) --

    An 8-tuple of costs for each kind of match or mismatch described in Covington's paper:

    • exact consonant or glide match

    • exact vowel match

    • vowel-vowel length mismatch or i and y or u and w

    • vowel-vowel mismatch

    • consonant-consonant mismatch

    • consonant-vowel mismatch

    • skip preceded by a skip

    • skip not preceded by a skip

    The weights used in Covington's first approximation can be used by supplying the tuple (0.0, 0.0, 0.5, 0.5, 0.5, 1.0, 0.5, 0.5)

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

alignment(src, tar)[source]

Return the top Covington alignment of two strings.

This returns only the top alignment in a standard (score, source alignment, target alignment) tuple format.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Covington score & alignment

Return type

tuple(float, str, str)

Examples

>>> cmp = Covington()
>>> cmp.alignment('hart', 'kordis')
(240, 'hart--', 'kordis')
>>> cmp.alignment('niy', 'genu')
(170, '--niy', 'genu-')

New in version 0.4.1.

alignments(src, tar, top_n=None)[source]

Return the Covington alignments of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • top_n (int) -- The number of alignments to return. If None, all alignments will be returned. If 0, all alignments with the top score will be returned.

Returns

Covington alignments

Return type

list

Examples

>>> cmp = Covington()
>>> cmp.alignments('hart', 'kordis', top_n=1)[0]
Alignment(src='hart--', tar='kordis', score=240)
>>> cmp.alignments('niy', 'genu', top_n=1)[0]
Alignment(src='--niy', tar='genu-', score=170)

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Covington distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Covington distance

Return type

float

Examples

>>> cmp = Covington()
>>> cmp.dist('cat', 'hat')
0.19117647058823528
>>> cmp.dist('Niall', 'Neil')
0.25555555555555554
>>> cmp.dist('aluminum', 'Catalan')
0.43333333333333335
>>> cmp.dist('ATCG', 'TAGC')
0.45454545454545453

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Covington distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Covington distance

Return type

float

Examples

>>> cmp = Covington()
>>> cmp.dist_abs('cat', 'hat')
65
>>> cmp.dist_abs('Niall', 'Neil')
115
>>> cmp.dist_abs('aluminum', 'Catalan')
325
>>> cmp.dist_abs('ATCG', 'TAGC')
200

New in version 0.4.0.

class abydos.distance.ALINE(epsilon=0, c_skip=-10, c_sub=35, c_exp=45, c_vwl=10, mode='local', phones='aline', normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._distance._Distance

ALINE alignment, similarity, and distance.

ALINE alignment was developed by [Kon00][Kon02][DHC+08], and establishes an alignment algorithm based on multivalued phonetic features and feature salience weights. Along with the alignment itself, the algorithm produces a term similarity score.

[DHC+08] develops ALINE's similarity score into a similarity measure & distance measure:

\[sim_{ALINE} = \frac{2 \dot score_{ALINE}(src, tar)} {score_{ALINE}(src, src) + score_{ALINE}(tar, tar)}\]

However, because the average of the two self-similarity scores is not guaranteed to be greater than or equal to the similarity score between the two strings, by default, this formula is not used here in order to guarantee that the similarity measure is bounded to [0, 1]. Instead, Kondrak's similarity measure is employed:

\[sim_{ALINE} = \frac{score_{ALINE}(src, tar)} {max(score_{ALINE}(src, src), score_{ALINE}(tar, tar))}\]

New in version 0.4.0.

Initialize ALINE instance.

Parameters
  • epsilon (float) -- The portion (out of 1.0) of the maximum ALINE score, above which alignments are returned. If set to 0, only the alignments matching the maximum alignment score are returned. If set to 1, all alignments scoring 0 or higher are returned.

  • c_skip (int) -- The cost of an insertion or deletion

  • c_sub (int) -- The cost of a substitution

  • c_exp (int) -- The cost of an expansion or contraction

  • c_vwl (int) -- The additional cost of a vowel substitution, expansion, or contraction

  • mode (str) -- Alignment mode, which can be local (default), global, half-local, or semi-global

  • phones (str) --

    Phonetic symbol set, which can be:
    • aline selects Kondrak's original symbols set

    • ipa selects IPA symbols

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). For the normalization proposed by Downey, et al. (2008), set this to: lambda x: sum(x)/len(x)

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

alignment(src, tar)[source]

Return the top ALINE alignment of two strings.

The top ALINE alignment is the first alignment with the best score. The purpose of this function is to have a single tuple as a return value.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

ALINE alignment and its score

Return type

tuple(float, str, str)

Examples

>>> cmp = ALINE()
>>> cmp.alignment('cat', 'hat')
(50.0, 'c ‖ a t ‖', 'h ‖ a t ‖')
>>> cmp.alignment('niall', 'neil')
(90.0, '‖ n i a ll ‖', '‖ n e i l  ‖')
>>> cmp.alignment('aluminum', 'catalan')
(81.5, '‖ a l u m ‖ inum', 'cat ‖ a l a n ‖')
>>> cmp.alignment('atcg', 'tagc')
(65.0, '‖ a t c ‖ g', 't ‖ a g c ‖')

New in version 0.4.1.

alignments(src, tar, score_only=False)[source]

Return the ALINE alignments of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • score_only (bool) -- Return the score only, not the alignments

Returns

ALINE alignments and their scores or the top score

Return type

list(tuple(float, str, str) or float

Examples

>>> cmp = ALINE()
>>> cmp.alignments('cat', 'hat')
[(50.0, 'c ‖ a t ‖', 'h ‖ a t ‖')]
>>> cmp.alignments('niall', 'neil')
[(90.0, '‖ n i a ll ‖', '‖ n e i l  ‖')]
>>> cmp.alignments('aluminum', 'catalan')
[(81.5, '‖ a l u m ‖ inum', 'cat ‖ a l a n ‖')]
>>> cmp.alignments('atcg', 'tagc')
[(65.0, '‖ a t c ‖ g', 't ‖ a g c ‖'), (65.0, 'a ‖ tc - g ‖',
'‖ t  a g ‖ c')]

New in version 0.4.0.

Changed in version 0.4.1: Renamed from .alignment to .alignments

c_features = {'aspirated', 'lateral', 'manner', 'nasal', 'place', 'retroflex', 'syllabic', 'voice'}
feature_weights = {'affricate': 0.9, 'alveolar': 0.85, 'approximant': 0.6, 'back': 0.0, 'bilabial': 1.0, 'central': 0.5, 'dental': 0.9, 'fricative': 0.8, 'front': 1.0, 'glottal': 0.1, 'high': 1.0, 'high vowel': 0.4, 'labiodental': 0.95, 'low': 0.0, 'low vowel': 0.0, 'mid': 0.5, 'mid vowel': 0.2, 'minus': 0.0, 'palatal': 0.7, 'palato-alveolar': 0.75, 'pharyngeal': 0.3, 'plus': 1.0, 'retroflex': 0.8, 'stop': 1.0, 'tap': 0.5, 'trill': 0.55, 'uvular': 0.5, 'velar': 0.6}
phones_ipa = {'a': {'aspirated': 'minus', 'back': 'front', 'high': 'low', 'lateral': 'minus', 'long': 'minus', 'manner': 'low vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'b': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'c': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'd': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'e': {'aspirated': 'minus', 'back': 'front', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'f': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'labiodental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'g': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'h': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'glottal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'i': {'aspirated': 'minus', 'back': 'front', 'high': 'high', 'lateral': 'minus', 'long': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'j': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'k': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'l': {'aspirated': 'minus', 'lateral': 'plus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'm': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'n': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'o': {'aspirated': 'minus', 'back': 'back', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'p': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'q': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'uvular', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'r': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'trill', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 's': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 't': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'u': {'aspirated': 'minus', 'back': 'back', 'high': 'high', 'lateral': 'minus', 'long': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'v': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'labiodental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'w': {'aspirated': 'minus', 'double': 'bilabial', 'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'x': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'y': {'aspirated': 'minus', 'back': 'front', 'high': 'high', 'lateral': 'minus', 'long': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'z': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'æ': {'aspirated': 'minus', 'back': 'front', 'high': 'low', 'lateral': 'minus', 'long': 'minus', 'manner': 'low vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'ç': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'ð': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'dental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ø': {'aspirated': 'minus', 'back': 'front', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'ħ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'pharyngeal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'ŋ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'œ': {'aspirated': 'minus', 'back': 'front', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'ɒ': {'aspirated': 'minus', 'back': 'back', 'high': 'low', 'lateral': 'minus', 'long': 'minus', 'manner': 'low vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'ɔ': {'aspirated': 'minus', 'back': 'back', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'ɖ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 'ə': {'aspirated': 'minus', 'back': 'central', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'ɛ': {'aspirated': 'minus', 'back': 'front', 'high': 'mid', 'lateral': 'minus', 'long': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'ɟ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɢ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'uvular', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɣ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɦ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'glottal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɨ': {'aspirated': 'minus', 'back': 'central', 'high': 'high', 'lateral': 'minus', 'long': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'ɬ': {'aspirated': 'minus', 'lateral': 'plus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'ɮ': {'aspirated': 'minus', 'lateral': 'plus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɰ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɱ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'labiodental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɲ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'palatal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɳ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɴ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'uvular', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɸ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'ɹ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɻ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɽ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'tap', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 'ɾ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'tap', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʀ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'trill', 'nasal': 'minus', 'place': 'uvular', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʁ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'uvular', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʂ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'minus'}, 'ʃ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'palato-alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'ʈ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'minus'}, 'ʉ': {'aspirated': 'minus', 'back': 'central', 'high': 'high', 'lateral': 'minus', 'long': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'ʋ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'labiodental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʐ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʒ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'palato-alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʔ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'glottal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'ʕ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'pharyngeal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʙ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'trill', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʝ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'ʰ': {'aspirated': 'plus', 'supplemental': True}, 'ː': {'long': 'plus', 'supplemental': True}, 'β': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'θ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'dental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'χ': {'aspirated': 'minus', 'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'uvular', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}}
phones_kondrak = {'A': {'aspirated': 'plus', 'supplemental': True}, 'B': {'back': 'back', 'supplemental': True}, 'C': {'back': 'central', 'supplemental': True}, 'D': {'place': 'dental', 'supplemental': True}, 'F': {'back': 'front', 'supplemental': True}, 'H': {'long': 'plus', 'supplemental': True}, 'N': {'nasal': 'plus', 'supplemental': True}, 'P': {'place': 'palatal', 'supplemental': True}, 'R': {'round': 'plus', 'supplemental': True}, 'S': {'manner': 'fricative', 'supplemental': True}, 'V': {'place': 'palato-alveolar', 'supplemental': True}, 'a': {'back': 'central', 'high': 'low', 'lateral': 'minus', 'manner': 'low vowel', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'b': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'c': {'lateral': 'minus', 'manner': 'affricate', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'd': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'e': {'back': 'front', 'high': 'mid', 'lateral': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'f': {'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'labiodental', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'g': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'h': {'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'glottal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'i': {'back': 'front', 'high': 'high', 'lateral': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'place': 'palatal', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'j': {'lateral': 'minus', 'manner': 'affricate', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'k': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'l': {'lateral': 'plus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'm': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'n': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'plus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}, 'o': {'back': 'back', 'high': 'mid', 'lateral': 'minus', 'manner': 'mid vowel', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'p': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'bilabial', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'q': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'glottal', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'r': {'lateral': 'minus', 'manner': 'approximant', 'nasal': 'minus', 'place': 'retroflex', 'retroflex': 'plus', 'syllabic': 'minus', 'voice': 'plus'}, 's': {'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 't': {'lateral': 'minus', 'manner': 'stop', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'u': {'back': 'back', 'high': 'high', 'lateral': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'v': {'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'labiodental', 'retroflex': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'w': {'back': 'back', 'double': 'bilabial', 'high': 'high', 'lateral': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'round': 'plus', 'syllabic': 'plus', 'voice': 'plus'}, 'x': {'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'minus'}, 'y': {'back': 'front', 'high': 'high', 'lateral': 'minus', 'manner': 'high vowel', 'nasal': 'minus', 'place': 'velar', 'retroflex': 'minus', 'round': 'minus', 'syllabic': 'plus', 'voice': 'plus'}, 'z': {'lateral': 'minus', 'manner': 'fricative', 'nasal': 'minus', 'place': 'alveolar', 'retroflex': 'minus', 'syllabic': 'minus', 'voice': 'plus'}}
salience = {'aspirated': 5, 'back': 5, 'high': 5, 'lateral': 10, 'long': 1, 'manner': 50, 'nasal': 10, 'place': 40, 'retroflex': 10, 'round': 5, 'syllabic': 5, 'voice': 10}
sim(src, tar)[source]

Return the normalized ALINE similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized ALINE similarity

Return type

float

Examples

>>> cmp = ALINE()
>>> cmp.dist('cat', 'hat')
0.4117647058823529
>>> cmp.dist('niall', 'neil')
0.33333333333333337
>>> cmp.dist('aluminum', 'catalan')
0.5925
>>> cmp.dist('atcg', 'tagc')
0.45833333333333337

New in version 0.4.0.

sim_score(src, tar)[source]

Return the ALINE alignment score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

ALINE alignment score

Return type

float

Examples

>>> cmp = ALINE()
>>> cmp.sim_score('cat', 'hat')
50.0
>>> cmp.sim_score('niall', 'neil')
90.0
>>> cmp.sim_score('aluminum', 'catalan')
81.5
>>> cmp.sim_score('atcg', 'tagc')
65.0

New in version 0.4.0.

v_features = {'back', 'high', 'long', 'nasal', 'retroflex', 'round', 'syllabic'}
class abydos.distance.FlexMetric(normalizer=<built-in function max>, indel_costs=None, subst_costs=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

FlexMetric distance.

FlexMetric distance [Kem05]

New in version 0.4.0.

Initialize FlexMetric instance.

Parameters
  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • indel_costs (list of tuples) -- A list of insertion and deletion costs. Each list element should be a tuple consisting of an iterable (sets are best) and a float value. The iterable consists of those letters whose insertion or deletion has a cost equal to the float value.

  • subst_costs (list of tuples) -- A list of substitution costs. Each list element should be a tuple consisting of an iterable (sets are best) and a float value. The iterable consists of the letters in each letter class, which may be substituted for each other at cost equal to the float value.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized FlexMetric distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized FlexMetric distance

Return type

float

Examples

>>> cmp = FlexMetric()
>>> cmp.dist('cat', 'hat')
0.26666666666666666
>>> cmp.dist('Niall', 'Neil')
0.3
>>> cmp.dist('aluminum', 'Catalan')
0.8375
>>> cmp.dist('ATCG', 'TAGC')
0.5499999999999999

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the FlexMetric distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

FlexMetric distance

Return type

float

Examples

>>> cmp = FlexMetric()
>>> cmp.dist_abs('cat', 'hat')
0.8
>>> cmp.dist_abs('Niall', 'Neil')
1.5
>>> cmp.dist_abs('aluminum', 'Catalan')
6.7
>>> cmp.dist_abs('ATCG', 'TAGC')
2.1999999999999997

New in version 0.4.0.

class abydos.distance.BISIM(qval=2, **kwargs)[source]

Bases: abydos.distance._distance._Distance

BI-SIM similarity.

BI-SIM similarity [KD03] is an n-gram based, edit-distance derived similarity measure.

New in version 0.4.0.

Initialize BISIM instance.

Parameters
  • qval (int) -- The number of characters to consider in each n-gram (q-gram). By default this is 2, hence BI-SIM. But TRI-SIM can be calculated by setting this to 3.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the BI-SIM similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

BI-SIM similarity

Return type

float

Examples

>>> cmp = BISIM()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.4
>>> cmp.sim('aluminum', 'Catalan')
0.3125
>>> cmp.sim('ATCG', 'TAGC')
0.375

New in version 0.4.0.

class abydos.distance.DiscountedLevenshtein(mode='lev', normalizer=<built-in function max>, discount_from=1, discount_func='log', vowels='aeiou', **kwargs)[source]

Bases: abydos.distance._levenshtein.Levenshtein

Discounted Levenshtein distance.

This is a variant of Levenshtein distance for which edits later in a string have discounted cost, on the theory that earlier edits are less likely than later ones.

New in version 0.4.1.

Initialize DiscountedLevenshtein instance.

Parameters
  • mode (str) --

    Specifies a mode for computing the discounted Levenshtein distance:

    • lev (default) computes the ordinary Levenshtein distance, in which edits may include inserts, deletes, and substitutions

    • osa computes the Optimal String Alignment distance, in which edits may include inserts, deletes, substitutions, and transpositions but substrings may only be edited once

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • discount_from (int or str) -- If an int is supplied, this is the first character whose edit cost will be discounted. If the str coda is supplied, discounting will start with the first non-vowel after the first vowel (the first syllable coda).

  • discount_func (str or function) -- The two supported str arguments are log, for a logarithmic discount function, and exp for a exponential discount function. See notes below for information on how to supply your own discount function.

  • vowels (str) -- These are the letters to consider as vowels when discount_from is set to coda. It defaults to the English vowels 'aeiou', but it would be reasonable to localize this to other languages or to add orthographic semi-vowels like 'y', 'w', and even 'h'.

  • **kwargs -- Arbitrary keyword arguments

Notes

This class is highly experimental and will need additional tuning.

The discount function can be passed as a callable function. It should expect an integer as its only argument and return a float, ideally less than or equal to 1.0. The argument represents the degree of discounting to apply.

New in version 0.4.1.

dist(src, tar)[source]

Return the normalized Levenshtein distance between two strings.

The Levenshtein distance is normalized by dividing the Levenshtein distance (calculated by any of the three supported methods) by the greater of the number of characters in src times the cost of a delete and the number of characters in tar times the cost of an insert. For the case in which all operations have \(cost = 1\), this is equivalent to the greater of the length of the two strings src & tar.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Levenshtein distance between src & tar

Return type

float

Examples

>>> cmp = DiscountedLevenshtein()
>>> cmp.dist('cat', 'hat')
0.3513958291799864
>>> cmp.dist('Niall', 'Neil')
0.5909885886270658
>>> cmp.dist('aluminum', 'Catalan')
0.8348163322045603
>>> cmp.dist('ATCG', 'TAGC')
0.7217609721523955

New in version 0.4.1.

dist_abs(src, tar)[source]

Return the Levenshtein distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Levenshtein distance between src & tar

Return type

float (may return a float if cost has float values)

Examples

>>> cmp = DiscountedLevenshtein()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
2.526064024369237
>>> cmp.dist_abs('aluminum', 'Catalan')
5.053867269967515
>>> cmp.dist_abs('ATCG', 'TAGC')
2.594032108779918
>>> cmp = DiscountedLevenshtein(mode='osa')
>>> cmp.dist_abs('ATCG', 'TAGC')
1.7482385137517997
>>> cmp.dist_abs('ACTG', 'TAGC')
3.342270622531718

New in version 0.4.1.

class abydos.distance.PhoneticEditDistance(mode='lev', cost=(1, 1, 1, 0.33333), normalizer=<built-in function max>, weights=None, **kwargs)[source]

Bases: abydos.distance._levenshtein.Levenshtein

Phonetic edit distance.

This is a variation on Levenshtein edit distance, intended for strings in IPA, that compares individual phones based on their featural similarity.

New in version 0.4.1.

Initialize PhoneticEditDistance instance.

Parameters
  • mode (str) --

    Specifies a mode for computing the edit distance:

    • lev (default) computes the ordinary Levenshtein distance, in which edits may include inserts, deletes, and substitutions

    • osa computes the Optimal String Alignment distance, in which edits may include inserts, deletes, substitutions, and transpositions but substrings may only be edited once

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and transpositions, respectively (by default: (1, 1, 1, 0.33333)). Note that transpositions cost a relatively low 0.33333. If this were 1.0, no phones would ever be transposed under the normal weighting, since even quite dissimilar phones such as [a] and [p] still agree in nearly 63% of their features.

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • weights (None or list or tuple or dict) -- If None, all features are of equal significance and a simple normalized hamming distance of the features is calculated. If a list or tuple of numeric values is supplied, the values are inferred as the weights for each feature, in order of the features listed in abydos.phones._phones._FEATURE_MASK. If a dict is supplied, its key values should match keys in abydos.phones._phones._FEATURE_MASK to which each weight (value) should be assigned. Missing values in all cases are assigned a weight of 0 and will be omitted from the comparison.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist(src, tar)[source]

Return the normalized phonetic edit distance between two strings.

The edit distance is normalized by dividing the edit distance (calculated by either of the two supported methods) by the greater of the number of characters in src times the cost of a delete and the number of characters in tar times the cost of an insert. For the case in which all operations have \(cost = 1\), this is equivalent to the greater of the length of the two strings src & tar.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Levenshtein distance between src & tar

Return type

float

Examples

>>> cmp = PhoneticEditDistance()
>>> round(cmp.dist('cat', 'hat'), 12)
0.059139784946
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.232258064516
>>> cmp.dist('aluminum', 'Catalan')
0.3084677419354839
>>> cmp.dist('ATCG', 'TAGC')
0.2983870967741935

New in version 0.4.1.

dist_abs(src, tar)[source]

Return the phonetic edit distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The phonetic edit distance between src & tar

Return type

int (may return a float if cost has float values)

Examples

>>> cmp = PhoneticEditDistance()
>>> cmp.dist_abs('cat', 'hat')
0.17741935483870974
>>> cmp.dist_abs('Niall', 'Neil')
1.161290322580645
>>> cmp.dist_abs('aluminum', 'Catalan')
2.467741935483871
>>> cmp.dist_abs('ATCG', 'TAGC')
1.193548387096774
>>> cmp = PhoneticEditDistance(mode='osa')
>>> cmp.dist_abs('ATCG', 'TAGC')
0.46236225806451603
>>> cmp.dist_abs('ACTG', 'TAGC')
1.2580645161290323

New in version 0.4.1.

class abydos.distance.Hamming(diff_lens=True, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Hamming distance.

Hamming distance [Ham50] equals the number of character positions at which two strings differ. For strings of unequal lengths, it is not normally defined. By default, this implementation calculates the Hamming distance of the first n characters where n is the lesser of the two strings' lengths and adds to this the difference in string lengths.

New in version 0.3.6.

Initialize Hamming instance.

Parameters
  • diff_lens (bool) -- If True (default), this returns the Hamming distance for those characters that have a matching character in both strings plus the difference in the strings' lengths. This is equivalent to extending the shorter string with obligatorily non-matching characters. If False, an exception is raised in the case of strings of unequal lengths.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Hamming distance between two strings.

Hamming distance normalized to the interval [0, 1].

The Hamming distance is normalized by dividing it by the greater of the number of characters in src & tar (unless diff_lens is set to False, in which case an exception is raised).

The arguments are identical to those of the hamming() function.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Hamming distance

Return type

float

Examples

>>> cmp = Hamming()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> cmp.dist('Niall', 'Neil')
0.6
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the Hamming distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Hamming distance between src & tar

Return type

int

Raises

ValueError -- Undefined for sequences of unequal length; set diff_lens to True for Hamming distance between strings of unequal lengths.

Examples

>>> cmp = Hamming()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
8
>>> cmp.dist_abs('ATCG', 'TAGC')
4

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.hamming(src, tar, diff_lens=True)[source]

Return the Hamming distance between two strings.

This is a wrapper for Hamming.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • diff_lens (bool) -- If True (default), this returns the Hamming distance for those characters that have a matching character in both strings plus the difference in the strings' lengths. This is equivalent to extending the shorter string with obligatorily non-matching characters. If False, an exception is raised in the case of strings of unequal lengths.

Returns

The Hamming distance between src & tar

Return type

int

Examples

>>> hamming('cat', 'hat')
1
>>> hamming('Niall', 'Neil')
3
>>> hamming('aluminum', 'Catalan')
8
>>> hamming('ATCG', 'TAGC')
4

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Hamming.dist_abs method instead.

abydos.distance.dist_hamming(src, tar, diff_lens=True)[source]

Return the normalized Hamming distance between two strings.

This is a wrapper for Hamming.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • diff_lens (bool) -- If True (default), this returns the Hamming distance for those characters that have a matching character in both strings plus the difference in the strings' lengths. This is equivalent to extending the shorter string with obligatorily non-matching characters. If False, an exception is raised in the case of strings of unequal lengths.

Returns

The normalized Hamming distance

Return type

float

Examples

>>> round(dist_hamming('cat', 'hat'), 12)
0.333333333333
>>> dist_hamming('Niall', 'Neil')
0.6
>>> dist_hamming('aluminum', 'Catalan')
1.0
>>> dist_hamming('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Hamming.dist method instead.

abydos.distance.sim_hamming(src, tar, diff_lens=True)[source]

Return the normalized Hamming similarity of two strings.

This is a wrapper for Hamming.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • diff_lens (bool) -- If True (default), this returns the Hamming distance for those characters that have a matching character in both strings plus the difference in the strings' lengths. This is equivalent to extending the shorter string with obligatorily non-matching characters. If False, an exception is raised in the case of strings of unequal lengths.

Returns

The normalized Hamming similarity

Return type

float

Examples

>>> round(sim_hamming('cat', 'hat'), 12)
0.666666666667
>>> sim_hamming('Niall', 'Neil')
0.4
>>> sim_hamming('aluminum', 'Catalan')
0.0
>>> sim_hamming('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Hamming.sim method instead.

class abydos.distance.MLIPNS(threshold=0.25, max_mismatches=2, **kwargs)[source]

Bases: abydos.distance._distance._Distance

MLIPNS similarity.

Modified Language-Independent Product Name Search (MLIPNS) is described in [SA10]. This function returns only 1.0 (similar) or 0.0 (not similar). LIPNS similarity is identical to normalized Hamming similarity.

New in version 0.3.6.

Initialize MLIPNS instance.

Parameters
  • threshold (float) -- A number [0, 1] indicating the maximum similarity score, below which the strings are considered 'similar' (0.25 by default)

  • max_mismatches (int) -- A number indicating the allowable number of mismatches to remove before declaring two strings not similar (2 by default)

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the MLIPNS similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

MLIPNS similarity

Return type

float

Examples

>>> sim_mlipns('cat', 'hat')
1.0
>>> sim_mlipns('Niall', 'Neil')
0.0
>>> sim_mlipns('aluminum', 'Catalan')
0.0
>>> sim_mlipns('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_mlipns(src, tar, threshold=0.25, max_mismatches=2)[source]

Return the MLIPNS distance between two strings.

This is a wrapper for MLIPNS.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • threshold (float) -- A number [0, 1] indicating the maximum similarity score, below which the strings are considered 'similar' (0.25 by default)

  • max_mismatches (int) -- A number indicating the allowable number of mismatches to remove before declaring two strings not similar (2 by default)

Returns

MLIPNS distance

Return type

float

Examples

>>> dist_mlipns('cat', 'hat')
0.0
>>> dist_mlipns('Niall', 'Neil')
1.0
>>> dist_mlipns('aluminum', 'Catalan')
1.0
>>> dist_mlipns('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MLIPNS.dist method instead.

abydos.distance.sim_mlipns(src, tar, threshold=0.25, max_mismatches=2)[source]

Return the MLIPNS similarity of two strings.

This is a wrapper for MLIPNS.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • threshold (float) -- A number [0, 1] indicating the maximum similarity score, below which the strings are considered 'similar' (0.25 by default)

  • max_mismatches (int) -- A number indicating the allowable number of mismatches to remove before declaring two strings not similar (2 by default)

Returns

MLIPNS similarity

Return type

float

Examples

>>> sim_mlipns('cat', 'hat')
1.0
>>> sim_mlipns('Niall', 'Neil')
0.0
>>> sim_mlipns('aluminum', 'Catalan')
0.0
>>> sim_mlipns('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MLIPNS.sim method instead.

class abydos.distance.RelaxedHamming(tokenizer=None, maxdist=2, discount=0.2, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Relaxed Hamming distance.

This is a variant of Hamming distance in which positionally close matches are considered partially matching.

New in version 0.4.1.

Initialize DiscountedHamming instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • maxdist (int) -- The maximum distance to consider for discounting.

  • discount (float) -- The discount factor multiplied by the distance from the source string position.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.1.

dist(src, tar)[source]

Return the normalized relaxed Hamming distance between strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized relaxed Hamming distance

Return type

float

Examples

>>> cmp = RelaxedHamming()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> cmp.dist('Niall', 'Neil')
0.27999999999999997
>>> cmp.dist('aluminum', 'Catalan')
0.8
>>> cmp.dist('ATCG', 'TAGC')
0.2

New in version 0.4.1.

dist_abs(src, tar)[source]

Return the discounted Hamming distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Relaxed Hamming distance

Return type

float

Examples

>>> cmp = RelaxedHamming()
>>> cmp.dist_abs('cat', 'hat')
1.0
>>> cmp.dist_abs('Niall', 'Neil')
1.4
>>> cmp.dist_abs('aluminum', 'Catalan')
6.4
>>> cmp.dist_abs('ATCG', 'TAGC')
0.8

New in version 0.4.1.

class abydos.distance.Tichy(cost=(1, 1), **kwargs)[source]

Bases: abydos.distance._distance._Distance

Tichy edit distance.

Tichy described an algorithm, implemented below, in [Tic84]. Following this, [Cor03] identifies an interpretation of this algorithm's output as a distance measure, which is largely followed by the methods below.

Tichy's algorithm locates substrings of a string S to be copied in order to create a string T. The only other operation used by his algorithms for string reconstruction are add operations.

Notes

While [Cor03] counts only move operations to calculate distance, I give the option (enabled by default) of counting add operations as part of the distance measure. To ignore the cost of add operations, set the cost value to (1, 0), for example, when initializing the object. Further, in the case that S and T are identical, a distance of 0 will be returned, even though this would still be counted as a single move operation spanning the whole of string S.

New in version 0.4.0.

Initialize Tichy instance.

Parameters
  • cost (tuple) -- A 2-tuple representing the cost of the two possible edits: block moves and adds (by default: (1, 1))

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Tichy edit distance between two strings.

The Tichy distance is normalized by dividing the distance by the length of the tar string.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Tichy distance between src & tar

Return type

float

Examples

>>> cmp = Tichy()
>>> round(cmp.dist('cat', 'hat'), 12)
0.666666666667
>>> round(cmp.dist('Niall', 'Neil'), 12)
1.0
>>> cmp.dist('aluminum', 'Catalan')
0.8571428571428571
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Tichy distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Tichy distance between src & tar

Return type

int (may return a float if cost has float values)

Examples

>>> cmp = Tichy()
>>> cmp.dist_abs('cat', 'hat')
2
>>> cmp.dist_abs('Niall', 'Neil')
4
>>> cmp.dist_abs('aluminum', 'Catalan')
6
>>> cmp.dist_abs('ATCG', 'TAGC')
4

New in version 0.4.0.

class abydos.distance.BlockLevenshtein(cost=(1, 1, 1, 1), normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._levenshtein.Levenshtein

Levenshtein distance with block operations.

In addition to character-level insert, delete, and replace operations, this version of the Levenshtein distance supports block-level insert, delete, and replace, provided that the block occurs in both input strings.

New in version 0.4.0.

Initialize BlockLevenshtein instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized block Levenshtein distance between strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Levenshtein distance with blocks between src & tar

Return type

float

Examples

>>> cmp = BlockLevenshtein()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.6
>>> cmp.dist('aluminum', 'Catalan')
0.875
>>> cmp.dist('ATCG', 'TAGC')
0.75

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the block Levenshtein edit distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The block Levenshtein edit distance between src & tar

Return type

int

Examples

>>> cmp = BlockLevenshtein()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
7
>>> cmp.dist_abs('ATCG', 'TAGC')
3

New in version 0.4.0.

class abydos.distance.CormodeLZ(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Cormode's LZ distance.

Cormode's LZ distance [CPSV00][Cor03]

New in version 0.4.0.

Initialize CormodeLZ instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Cormode's LZ distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Cormode's LZ distance

Return type

float

Examples

>>> cmp = CormodeLZ()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.8
>>> cmp.dist('aluminum', 'Catalan')
0.625
>>> cmp.dist('ATCG', 'TAGC')
0.75

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Cormode's LZ distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Cormode's LZ distance

Return type

float

Examples

>>> cmp = CormodeLZ()
>>> cmp.dist_abs('cat', 'hat')
2
>>> cmp.dist_abs('Niall', 'Neil')
5
>>> cmp.dist_abs('aluminum', 'Catalan')
6
>>> cmp.dist_abs('ATCG', 'TAGC')
4

New in version 0.4.0.

class abydos.distance.JaroWinkler(qval=1, mode='winkler', long_strings=False, boost_threshold=0.7, scaling_factor=0.1, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Jaro-Winkler distance.

Jaro(-Winkler) distance is a string edit distance initially proposed by Jaro and extended by Winkler [Jar89][Win90].

This is Python based on the C code for strcmp95: http://web.archive.org/web/20110629121242/http://www.census.gov/geo/msb/stand/strcmp.c [WMJL94]. The above file is a US Government publication and, accordingly, in the public domain.

New in version 0.3.6.

Initialize JaroWinkler instance.

Parameters
  • qval (int) -- The length of each q-gram (defaults to 1: character-wise matching)

  • mode (str) --

    Indicates which variant of this distance metric to compute:

    • winkler -- computes the Jaro-Winkler distance (default) which increases the score for matches near the start of the word

    • jaro -- computes the Jaro distance

  • long_strings (bool) -- Set to True to "Increase the probability of a match when the number of matched characters is large. This option allows for a little more tolerance when the strings are large. It is not an appropriate test when comparing fixed length fields such as phone and social security numbers." (Used in 'winkler' mode only.)

  • boost_threshold (float) -- A value between 0 and 1, below which the Winkler boost is not applied (defaults to 0.7). (Used in 'winkler' mode only.)

  • scaling_factor (float) -- A value between 0 and 0.25, indicating by how much to boost scores for matching prefixes (defaults to 0.1). (Used in 'winkler' mode only.)

New in version 0.4.0.

sim(src, tar)[source]

Return the Jaro or Jaro-Winkler similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Jaro or Jaro-Winkler similarity

Return type

float

Raises
  • ValueError -- Unsupported boost_threshold assignment; boost_threshold must be between 0 and 1.

  • ValueError -- Unsupported scaling_factor assignment; scaling_factor must be between 0 and 0.25.'

Examples

>>> round(sim_jaro_winkler('cat', 'hat'), 12)
0.777777777778
>>> round(sim_jaro_winkler('Niall', 'Neil'), 12)
0.805
>>> round(sim_jaro_winkler('aluminum', 'Catalan'), 12)
0.60119047619
>>> round(sim_jaro_winkler('ATCG', 'TAGC'), 12)
0.833333333333
>>> round(sim_jaro_winkler('cat', 'hat', mode='jaro'), 12)
0.777777777778
>>> round(sim_jaro_winkler('Niall', 'Neil', mode='jaro'), 12)
0.783333333333
>>> round(sim_jaro_winkler('aluminum', 'Catalan', mode='jaro'), 12)
0.60119047619
>>> round(sim_jaro_winkler('ATCG', 'TAGC', mode='jaro'), 12)
0.833333333333

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_jaro_winkler(src, tar, qval=1, mode='winkler', long_strings=False, boost_threshold=0.7, scaling_factor=0.1)[source]

Return the Jaro or Jaro-Winkler distance between two strings.

This is a wrapper for JaroWinkler.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • qval (int) -- The length of each q-gram (defaults to 1: character-wise matching)

  • mode (str) --

    Indicates which variant of this distance metric to compute:

    • winkler -- computes the Jaro-Winkler distance (default) which increases the score for matches near the start of the word

    • jaro -- computes the Jaro distance

  • long_strings (bool) -- Set to True to "Increase the probability of a match when the number of matched characters is large. This option allows for a little more tolerance when the strings are large. It is not an appropriate test when comparing fixedlength fields such as phone and social security numbers." (Used in 'winkler' mode only.)

  • boost_threshold (float) -- A value between 0 and 1, below which the Winkler boost is not applied (defaults to 0.7). (Used in 'winkler' mode only.)

  • scaling_factor (float) -- A value between 0 and 0.25, indicating by how much to boost scores for matching prefixes (defaults to 0.1). (Used in 'winkler' mode only.)

Returns

Jaro or Jaro-Winkler distance

Return type

float

Examples

>>> round(dist_jaro_winkler('cat', 'hat'), 12)
0.222222222222
>>> round(dist_jaro_winkler('Niall', 'Neil'), 12)
0.195
>>> round(dist_jaro_winkler('aluminum', 'Catalan'), 12)
0.39880952381
>>> round(dist_jaro_winkler('ATCG', 'TAGC'), 12)
0.166666666667
>>> round(dist_jaro_winkler('cat', 'hat', mode='jaro'), 12)
0.222222222222
>>> round(dist_jaro_winkler('Niall', 'Neil', mode='jaro'), 12)
0.216666666667
>>> round(dist_jaro_winkler('aluminum', 'Catalan', mode='jaro'), 12)
0.39880952381
>>> round(dist_jaro_winkler('ATCG', 'TAGC', mode='jaro'), 12)
0.166666666667

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the JaroWinkler.dist method instead.

abydos.distance.sim_jaro_winkler(src, tar, qval=1, mode='winkler', long_strings=False, boost_threshold=0.7, scaling_factor=0.1)[source]

Return the Jaro or Jaro-Winkler similarity of two strings.

This is a wrapper for JaroWinkler.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • qval (int) -- The length of each q-gram (defaults to 1: character-wise matching)

  • mode (str) --

    Indicates which variant of this distance metric to compute:

    • winkler -- computes the Jaro-Winkler distance (default) which increases the score for matches near the start of the word

    • jaro -- computes the Jaro distance

  • long_strings (bool) -- Set to True to "Increase the probability of a match when the number of matched characters is large. This option allows for a little more tolerance when the strings are large. It is not an appropriate test when comparing fixedlength fields such as phone and social security numbers." (Used in 'winkler' mode only.)

  • boost_threshold (float) -- A value between 0 and 1, below which the Winkler boost is not applied (defaults to 0.7). (Used in 'winkler' mode only.)

  • scaling_factor (float) -- A value between 0 and 0.25, indicating by how much to boost scores for matching prefixes (defaults to 0.1). (Used in 'winkler' mode only.)

Returns

Jaro or Jaro-Winkler similarity

Return type

float

Examples

>>> round(sim_jaro_winkler('cat', 'hat'), 12)
0.777777777778
>>> round(sim_jaro_winkler('Niall', 'Neil'), 12)
0.805
>>> round(sim_jaro_winkler('aluminum', 'Catalan'), 12)
0.60119047619
>>> round(sim_jaro_winkler('ATCG', 'TAGC'), 12)
0.833333333333
>>> round(sim_jaro_winkler('cat', 'hat', mode='jaro'), 12)
0.777777777778
>>> round(sim_jaro_winkler('Niall', 'Neil', mode='jaro'), 12)
0.783333333333
>>> round(sim_jaro_winkler('aluminum', 'Catalan', mode='jaro'), 12)
0.60119047619
>>> round(sim_jaro_winkler('ATCG', 'TAGC', mode='jaro'), 12)
0.833333333333

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the JaroWinkler.sim method instead.

class abydos.distance.Strcmp95(long_strings=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Strcmp95.

This is a Python translation of the C code for strcmp95: http://web.archive.org/web/20110629121242/http://www.census.gov/geo/msb/stand/strcmp.c [WMJL94]. The above file is a US Government publication and, accordingly, in the public domain.

This is based on the Jaro-Winkler distance, but also attempts to correct for some common typos and frequently confused characters. It is also limited to uppercase ASCII characters, so it is appropriate to American names, but not much else.

New in version 0.3.6.

Initialize Strcmp95 instance.

Parameters
  • long_strings (bool) -- Set to True to increase the probability of a match when the number of matched characters is large. This option allows for a little more tolerance when the strings are large. It is not an appropriate test when comparing fixed length fields such as phone and social security numbers.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the strcmp95 similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Strcmp95 similarity

Return type

float

Examples

>>> cmp = Strcmp95()
>>> cmp.sim('cat', 'hat')
0.7777777777777777
>>> cmp.sim('Niall', 'Neil')
0.8454999999999999
>>> cmp.sim('aluminum', 'Catalan')
0.6547619047619048
>>> cmp.sim('ATCG', 'TAGC')
0.8333333333333334

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_strcmp95(src, tar, long_strings=False)[source]

Return the strcmp95 distance between two strings.

This is a wrapper for Strcmp95.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • long_strings (bool) -- Set to True to increase the probability of a match when the number of matched characters is large. This option allows for a little more tolerance when the strings are large. It is not an appropriate test when comparing fixed length fields such as phone and social security numbers.

Returns

Strcmp95 distance

Return type

float

Examples

>>> round(dist_strcmp95('cat', 'hat'), 12)
0.222222222222
>>> round(dist_strcmp95('Niall', 'Neil'), 12)
0.1545
>>> round(dist_strcmp95('aluminum', 'Catalan'), 12)
0.345238095238
>>> round(dist_strcmp95('ATCG', 'TAGC'), 12)
0.166666666667

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Strcmp95.dist method instead.

abydos.distance.sim_strcmp95(src, tar, long_strings=False)[source]

Return the strcmp95 similarity of two strings.

This is a wrapper for Strcmp95.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • long_strings (bool) -- Set to True to increase the probability of a match when the number of matched characters is large. This option allows for a little more tolerance when the strings are large. It is not an appropriate test when comparing fixed length fields such as phone and social security numbers.

Returns

Strcmp95 similarity

Return type

float

Examples

>>> sim_strcmp95('cat', 'hat')
0.7777777777777777
>>> sim_strcmp95('Niall', 'Neil')
0.8454999999999999
>>> sim_strcmp95('aluminum', 'Catalan')
0.6547619047619048
>>> sim_strcmp95('ATCG', 'TAGC')
0.8333333333333334

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Strcmp95.sim method instead.

class abydos.distance.IterativeSubString(hamacher=0.6, normalize_strings=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Iterative-SubString correlation.

Iterative-SubString (I-Sub) correlation [SSK05]

This is a straightforward port of the primary author's Java implementation: http://www.image.ece.ntua.gr/~gstoil/software/I_Sub.java

New in version 0.4.0.

Initialize IterativeSubString instance.

Parameters
  • hamacher (float) -- The constant factor for the Hamacher product

  • normalize_strings (bool) -- Normalize the strings by removing the characters in '._ ' and lower casing

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

corr(src, tar)[source]

Return the Iterative-SubString correlation of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Iterative-SubString correlation

Return type

float

Examples

>>> cmp = IterativeSubString()
>>> cmp.corr('cat', 'hat')
-1.0
>>> cmp.corr('Niall', 'Neil')
-0.9
>>> cmp.corr('aluminum', 'Catalan')
-1.0
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Iterative-SubString similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Iterative-SubString similarity

Return type

float

Examples

>>> cmp = IterativeSubString()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.04999999999999999
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.AMPLE(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

AMPLE similarity.

The AMPLE similarity [DLZ05][AZvanGemund07] is defined in getAverageSequenceWeight() in the AverageSequenceWeightEvaluator.java file of AMPLE's source code. For two sets X and Y and a population N, it is

\[sim_{AMPLE}(X, Y) = \big|\frac{|X \cap Y|}{|X|} - \frac{|Y \setminus X|}{|N \setminus X|}\big|\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{AMPLE} = \big|\frac{a}{a+b}-\frac{c}{c+d}\big|\]

Notes

This measure is asymmetric. The first ratio considers how similar the two strings are, while the second considers how dissimilar the second string is. As a result, both very similar and very dissimilar strings will score high on this measure, provided the unique aspects are present chiefly in the latter string.

New in version 0.4.0.

Initialize AMPLE instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the AMPLE similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

AMPLE similarity

Return type

float

Examples

>>> cmp = AMPLE()
>>> cmp.sim('cat', 'hat')
0.49743589743589745
>>> cmp.sim('Niall', 'Neil')
0.32947729220222793
>>> cmp.sim('aluminum', 'Catalan')
0.10209049255441008
>>> cmp.sim('ATCG', 'TAGC')
0.006418485237483954

New in version 0.4.0.

class abydos.distance.AZZOO(sigma=0.5, alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

AZZOO similarity.

For two sets X and Y, and alphabet N, and a parameter \(\sigma\), AZZOO similarity [CTY06] is

\[sim_{AZZOO_{\sigma}}(X, Y) = \sum{s_i}\]

where \(s_i = 1\) if \(X_i = Y_i = 1\), \(s_i = \sigma\) if \(X_i = Y_i = 0\), and \(s_i = 0\) otherwise.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{AZZOO} = a + \sigma \cdot d\]

New in version 0.4.0.

Initialize AZZOO instance.

Parameters
  • sigma (float) -- Sigma designates the contribution to similarity given by the 0-0 samples in the set.

  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the AZZOO similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

AZZOO similarity

Return type

float

Examples

>>> cmp = AZZOO()
>>> cmp.sim('cat', 'hat')
0.9923857868020305
>>> cmp.sim('Niall', 'Neil')
0.9860759493670886
>>> cmp.sim('aluminum', 'Catalan')
0.9710327455919395
>>> cmp.sim('ATCG', 'TAGC')
0.9809885931558935

New in version 0.4.0.

sim_score(src, tar)[source]

Return the AZZOO similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

AZZOO similarity

Return type

float

Examples

>>> cmp = AZZOO()
>>> cmp.sim_score('cat', 'hat')
391.0
>>> cmp.sim_score('Niall', 'Neil')
389.5
>>> cmp.sim_score('aluminum', 'Catalan')
385.5
>>> cmp.sim_score('ATCG', 'TAGC')
387.0

New in version 0.4.0.

class abydos.distance.Anderberg(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Anderberg's D.

For two sets X and Y and a population N, Anderberg's D [And73] is

\[\begin{split}t_1 = max(|X \cap Y|, |X \setminus Y|)+ max(|Y \setminus X|, |(N \setminus X) \setminus Y|)+\\ max(|X \cap Y|, |Y \setminus X|)+ max(|X \setminus Y|, |(N \setminus X) \setminus Y|)\\ \\ t_2 = max(|Y|, |N \setminus Y|)+max(|X|, |N \setminus X|)\\ \\ sim_{Anderberg}(X, Y) = \frac{t_1-t_2}{2|N|}\end{split}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Anderberg} = \frac{(max(a,b)+max(c,d)+max(a,c)+max(b,d))- (max(a+b,b+d)+max(a+b,c+d))}{2n}\]

Notes

There are various references to another "Anderberg similarity", \(sim_{Anderberg} = \frac{8a}{8a+b+c}\), but I cannot substantiate the claim that this appears in [And73]. In any case, if you want to use this measure, you may instatiate WeightedJaccard with weight=8.

Anderberg states that "[t]his quantity is the actual reduction in the error probability (also the actual increase in the correct prediction) as a consequence of using predictor information" [And73]. It ranges [0, 0.5] so a sim method ranging [0, 1] is provided in addition to sim_score, which gives the value D itself.

It is difficult to term this measure a similarity score. Identical strings often fail to gain high scores. Also, strings that would otherwise be considered quite similar often earn lower scores than those that are less similar.

New in version 0.4.0.

Initialize Anderberg instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Anderberg's D similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Anderberg similarity

Return type

float

Examples

>>> cmp = Anderberg()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Anderberg's D similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Anderberg similarity

Return type

float

Examples

>>> cmp = Anderberg()
>>> cmp.sim_score('cat', 'hat')
0.0
>>> cmp.sim_score('Niall', 'Neil')
0.0
>>> cmp.sim_score('aluminum', 'Catalan')
0.0
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.AndresMarzoDelta(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Andres & Marzo's Delta correlation.

For two sets X and Y and a population N, Andres & Marzo's \(\Delta\) correlation [AndresM04] is

\[corr_{AndresMarzo_\Delta}(X, Y) = \Delta = \frac{|X \cap Y| + |(N \setminus X) \setminus Y| - 2\sqrt{|X \setminus Y| \cdot |Y \setminus X|}}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{AndresMarzo_\Delta} = \Delta = \frac{a+d-2\sqrt{b \cdot c}}{n}\]

New in version 0.4.0.

Initialize AndresMarzoDelta instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Andres & Marzo's Delta correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Andres & Marzo's Delta correlation

Return type

float

Examples

>>> cmp = AndresMarzoDelta()
>>> cmp.corr('cat', 'hat')
0.9897959183673469
>>> cmp.corr('Niall', 'Neil')
0.9822344346552608
>>> cmp.corr('aluminum', 'Catalan')
0.9618259496215341
>>> cmp.corr('ATCG', 'TAGC')
0.9744897959183674

New in version 0.4.0.

sim(src, tar)[source]

Return the Andres & Marzo's Delta similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Andres & Marzo's Delta similarity

Return type

float

Examples

>>> cmp = AndresMarzoDelta()
>>> cmp.sim('cat', 'hat')
0.9948979591836735
>>> cmp.sim('Niall', 'Neil')
0.9911172173276304
>>> cmp.sim('aluminum', 'Catalan')
0.980912974810767
>>> cmp.sim('ATCG', 'TAGC')
0.9872448979591837

New in version 0.4.0.

class abydos.distance.BaroniUrbaniBuserI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baroni-Urbani & Buser I similarity.

For two sets X and Y and a population N, the Baroni-Urbani & Buser I similarity [BUB76] is

\[sim_{BaroniUrbaniBuserI}(X, Y) = \frac{\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + |X \cap Y|} {\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + |X \cap Y| + |X \setminus Y| + |Y \setminus X|}\]

This is the second, but more commonly used and referenced of the two similarities proposed by Baroni-Urbani & Buser.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{BaroniUrbaniBuserI} = \frac{\sqrt{ad}+a}{\sqrt{ad}+a+b+c}\]

New in version 0.4.0.

Initialize BaroniUrbaniBuserI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Baroni-Urbani & Buser I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baroni-Urbani & Buser I similarity

Return type

float

Examples

>>> cmp = BaroniUrbaniBuserI()
>>> cmp.sim('cat', 'hat')
0.9119837740878104
>>> cmp.sim('Niall', 'Neil')
0.8552823175014205
>>> cmp.sim('aluminum', 'Catalan')
0.656992712054851
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.BaroniUrbaniBuserII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baroni-Urbani & Buser II correlation.

For two sets X and Y and a population N, the Baroni-Urbani & Buser II correlation [BUB76] is

\[corr_{BaroniUrbaniBuserII}(X, Y) = \frac{\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + |X \cap Y| - |X \setminus Y| - |Y \setminus X|} {\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + |X \cap Y| + |X \setminus Y| + |Y \setminus X|}\]

This is the first, but less commonly used and referenced of the two similarities proposed by Baroni-Urbani & Buser.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{BaroniUrbaniBuserII} = \frac{\sqrt{ad}+a-b-c}{\sqrt{ad}+a+b+c}\]

New in version 0.4.0.

Initialize BaroniUrbaniBuserII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Baroni-Urbani & Buser II correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baroni-Urbani & Buser II correlation

Return type

float

Examples

>>> cmp = BaroniUrbaniBuserII()
>>> cmp.corr('cat', 'hat')
0.8239675481756209
>>> cmp.corr('Niall', 'Neil')
0.7105646350028408
>>> cmp.corr('aluminum', 'Catalan')
0.31398542410970204
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Baroni-Urbani & Buser II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baroni-Urbani & Buser II similarity

Return type

float

Examples

>>> cmp = BaroniUrbaniBuserII()
>>> cmp.sim('cat', 'hat')
0.9119837740878105
>>> cmp.sim('Niall', 'Neil')
0.8552823175014204
>>> cmp.sim('aluminum', 'Catalan')
0.656992712054851
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.BatageljBren(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Batagelj & Bren distance.

For two sets X and Y and a population N, the Batagelj & Bren distance [BB95], Batagelj & Bren's \(Q_0\), is

\[dist_{BatageljBren}(X, Y) = \frac{|X \setminus Y| \cdot |Y \setminus X|} {|X \cap Y| \cdot |(N \setminus X) \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BatageljBren} = \frac{bc}{ad}\]

New in version 0.4.0.

Initialize BatageljBren instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Batagelj & Bren distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Batagelj & Bren distance

Return type

float

Examples

>>> cmp = BatageljBren()
>>> cmp.dist('cat', 'hat')
3.2789465400556106e-06
>>> cmp.dist('Niall', 'Neil')
9.874917709019092e-06
>>> cmp.dist('aluminum', 'Catalan')
9.276668350823718e-05
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Batagelj & Bren distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Batagelj & Bren distance

Return type

float

Examples

>>> cmp = BatageljBren()
>>> cmp.dist_abs('cat', 'hat')
0.002570694087403599
>>> cmp.dist_abs('Niall', 'Neil')
0.007741935483870968
>>> cmp.dist_abs('aluminum', 'Catalan')
0.07282184655396619
>>> cmp.dist_abs('ATCG', 'TAGC')
inf

New in version 0.4.0.

class abydos.distance.BaulieuI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu I distance.

For two sets X and Y and a population N, Baulieu I distance [Bau89] is

\[sim_{BaulieuI}(X, Y) = \frac{|X| \cdot |Y| - |X \cap Y|^2}{|X| \cdot |Y|}\]

This is Baulieu's 12th dissimilarity coefficient.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{BaulieuI} = \frac{(a+b)(a+c)-a^2}{(a+b)(a+c)}\]

New in version 0.4.0.

Initialize BaulieuI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu I distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu I distance

Return type

float

Examples

>>> cmp = BaulieuI()
>>> cmp.dist('cat', 'hat')
0.75
>>> cmp.dist('Niall', 'Neil')
0.8666666666666667
>>> cmp.dist('aluminum', 'Catalan')
0.9861111111111112
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.BaulieuII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu II similarity.

For two sets X and Y and a population N, Baulieu II similarity [Bau89] is

\[sim_{BaulieuII}(X, Y) = \frac{|X \cap Y|^2 \cdot |(N \setminus X) \setminus Y|^2} {|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}\]

This is based on Baulieu's 13th dissimilarity coefficient.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{BaulieuII} = \frac{a^2d^2}{(a+b)(a+c)(b+d)(c+d)}\]

New in version 0.4.0.

Initialize BaulieuII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Baulieu II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu II similarity

Return type

float

Examples

>>> cmp = BaulieuII()
>>> cmp.sim('cat', 'hat')
0.24871959237343852
>>> cmp.sim('Niall', 'Neil')
0.13213719608444902
>>> cmp.sim('aluminum', 'Catalan')
0.013621892326789235
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.BaulieuIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu III distance.

For two sets X and Y and a population N, Baulieu III distance [Bau89] is

\[sim_{BaulieuIII}(X, Y) = \frac{|N|^2 - 4(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)}{2 \cdot |N|^2}\]

This is based on Baulieu's 20th dissimilarity coefficient.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{BaulieuIII} = \frac{n^2 - 4(ad-bc)}{2n^2}\]

Notes

It should be noted that this is based on Baulieu's 20th dissimilarity coefficient. This distance is exactly half Baulieu's 20th dissimilarity. According to [Bau89], the 20th dissimilarity should be a value in the range [0.0, 1.0], meeting the article's (P1) property, but the formula given ranges [0.0, 2.0], so dividing by 2 corrects the formula to meet the article's expectations.

New in version 0.4.0.

Initialize BaulieuIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu III distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu III distance

Return type

float

Examples

>>> cmp = BaulieuIII()
>>> cmp.dist('cat', 'hat')
0.4949500208246564
>>> cmp.dist('Niall', 'Neil')
0.4949955747605165
>>> cmp.dist('aluminum', 'Catalan')
0.49768591017891195
>>> cmp.dist('ATCG', 'TAGC')
0.5000813463140358

New in version 0.4.0.

class abydos.distance.BaulieuIV(alphabet=None, tokenizer=None, intersection_type='crisp', positive_irrational=2.718281828459045, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu IV distance.

For two sets X and Y, a population N, and a positive irractional number k, Baulieu IV distance [Bau97] is

\[dist_{BaulieuIV}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X| - (|X \cap Y| + \frac{1}{2}) \cdot (|(N \setminus X) \setminus Y| + \frac{1}{2}) \cdot |(N \setminus X) \setminus Y| \cdot k}{|N|}\]

This is Baulieu's 22nd dissimilarity coefficient.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuIV} = \frac{b+c-(a+\frac{1}{2})(d+\frac{1}{2})dk}{n}\]

Notes

The default value of k is Euler's number \(e\), but other irrationals such as \(\pi\) or \(\sqrt{2}\) could be substituted at initialization.

New in version 0.4.0.

Initialize BaulieuIV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Baulieu IV distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Baulieu IV distance

Return type

float

Examples

>>> cmp = BaulieuIV()
>>> cmp.dist('cat', 'hat')
0.49999799606535283
>>> cmp.dist('Niall', 'Neil')
0.49999801148659684
>>> cmp.dist('aluminum', 'Catalan')
0.49999883126809364
>>> cmp.dist('ATCG', 'TAGC')
0.4999996033268451

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Baulieu IV distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu IV distance

Return type

float

Examples

>>> cmp = BaulieuIV()
>>> cmp.dist_abs('cat', 'hat')
-5249.96272285802
>>> cmp.dist_abs('Niall', 'Neil')
-5209.561726488335
>>> cmp.dist_abs('aluminum', 'Catalan')
-3073.6070822721244
>>> cmp.dist_abs('ATCG', 'TAGC')
-1039.2151656463932

New in version 0.4.0.

class abydos.distance.BaulieuV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu V distance.

For two sets X and Y and a population N, Baulieu V distance [Bau97] is

\[dist_{BaulieuV}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X| + 1}{|X \cap Y| + |X \setminus Y| + |Y \setminus X| + 1}\]

This is Baulieu's 23rd dissimilarity coefficient. This coefficient fails Baulieu's (P2) property, that \(D(a,0,0,0) = 0\). Rather, \(D(a,0,0,0) > 0\), but \(\lim_{a \to \infty} D(a,0,0,0) = 0\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuV} = \frac{b+c+1}{a+b+c+1}\]

New in version 0.4.0.

Initialize BaulieuV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu V distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu V distance

Return type

float

Examples

>>> cmp = BaulieuV()
>>> cmp.dist('cat', 'hat')
0.7142857142857143
>>> cmp.dist('Niall', 'Neil')
0.8
>>> cmp.dist('aluminum', 'Catalan')
0.9411764705882353
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.BaulieuVI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu VI distance.

For two sets X and Y and a population N, Baulieu VI distance [Bau97] is

\[dist_{BaulieuVI}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X|} {|X \cap Y| + |X \setminus Y| + |Y \setminus X| + 1}\]

This is Baulieu's 24th dissimilarity coefficient. This coefficient fails Baulieu's (P3) property, that \(D(a,b,c,d) = 1\) for some (a,b,c,d). Rather, \(D(a,b,c,d) < 1\), but \(\lim_{b \to \infty, c \to \infty} D(a,b,c,d) = 0\) for \(a = 0\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuVI} = \frac{b+c}{a+b+c+1}\]

New in version 0.4.0.

Initialize BaulieuVI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu VI distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu VI distance

Return type

float

Examples

>>> cmp = BaulieuVI()
>>> cmp.dist('cat', 'hat')
0.5714285714285714
>>> cmp.dist('Niall', 'Neil')
0.7
>>> cmp.dist('aluminum', 'Catalan')
0.8823529411764706
>>> cmp.dist('ATCG', 'TAGC')
0.9090909090909091

New in version 0.4.0.

class abydos.distance.BaulieuVII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu VII distance.

For two sets X and Y and a population N, Baulieu VII distance [Bau97] is

\[dist_{BaulieuVII}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X|} {|N| + |X \cap Y| \cdot (|X \cap Y| - 4)^2}\]

This is Baulieu's 25th dissimilarity coefficient. This coefficient fails Baulieu's (P4) property, that \(D(a+1,b,c,d) \leq D(a,b,c,d) = 0\) with equality holding iff \(D(a,b,c,d) = 0\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuVII} = \frac{b+c}{n + a \cdot (a-4)^2}\]

New in version 0.4.0.

Initialize BaulieuVII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu VII distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu VII distance

Return type

float

Examples

>>> cmp = BaulieuVII()
>>> cmp.dist('cat', 'hat')
0.005050505050505051
>>> cmp.dist('Niall', 'Neil')
0.008838383838383838
>>> cmp.dist('aluminum', 'Catalan')
0.018891687657430732
>>> cmp.dist('ATCG', 'TAGC')
0.012755102040816327

New in version 0.4.0.

class abydos.distance.BaulieuVIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu VIII distance.

For two sets X and Y and a population N, Baulieu VIII distance [Bau97] is

\[dist_{BaulieuVIII}(X, Y) = \frac{(|X \setminus Y| - |Y \setminus X|)^2}{|N|^2}\]

This is Baulieu's 26th dissimilarity coefficient. This coefficient fails Baulieu's (P5) property, that \(D(a,b+1,c,d) \geq D(a,b,c,d)\), with equality holding if \(D(a,b,c,d) = 1\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuVIII} = \frac{(b-c)^2}{n^2}\]

New in version 0.4.0.

Initialize BaulieuVIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu VIII distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu VIII distance

Return type

float

Examples

>>> cmp = BaulieuVIII()
>>> cmp.dist('cat', 'hat')
0.0
>>> cmp.dist('Niall', 'Neil')
1.6269262807163682e-06
>>> cmp.dist('aluminum', 'Catalan')
1.6227838857560144e-06
>>> cmp.dist('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.BaulieuIX(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu IX distance.

For two sets X and Y and a population N, Baulieu IX distance [Bau97] is

\[dist_{BaulieuIX}(X, Y) = \frac{|X \setminus Y| + 2 \cdot |Y \setminus X|}{|N| + |Y \setminus X|}\]

This is Baulieu's 27th dissimilarity coefficient. This coefficient fails Baulieu's (P7) property, that \(D(a,b,c,d) = D(a,c,b,d)\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuIX} = \frac{b+2c}{a+b+2c+d}\]

New in version 0.4.0.

Initialize BaulieuIX instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu IX distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu IX distance

Return type

float

Examples

>>> cmp = BaulieuIX()
>>> cmp.dist('cat', 'hat')
0.007633587786259542
>>> cmp.dist('Niall', 'Neil')
0.012706480304955527
>>> cmp.dist('aluminum', 'Catalan')
0.027777777777777776
>>> cmp.dist('ATCG', 'TAGC')
0.019011406844106463

New in version 0.4.0.

class abydos.distance.BaulieuX(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu X distance.

For two sets X and Y and a population N, Baulieu X distance [Bau97] is

\[dist_{BaulieuX}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X| + max(|X \setminus Y|, |Y \setminus X|)}{|N| + max(|X \setminus Y|, |Y \setminus X|)}\]

This is Baulieu's 28th dissimilarity coefficient. This coefficient fails Baulieu's (P8) property, that \(D\) is a rational function whose numerator and denominator are both (total) linear.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuX} = \frac{b+c+max(b,c)}{n+max(b,c)}\]

New in version 0.4.0.

Initialize BaulieuX instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu X distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu X distance

Return type

float

Examples

>>> cmp = BaulieuX()
>>> cmp.dist('cat', 'hat')
0.007633587786259542
>>> cmp.dist('Niall', 'Neil')
0.013959390862944163
>>> cmp.dist('aluminum', 'Catalan')
0.029003783102143757
>>> cmp.dist('ATCG', 'TAGC')
0.019011406844106463

New in version 0.4.0.

class abydos.distance.BaulieuXI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu XI distance.

For two sets X and Y and a population N, Baulieu XI distance [Bau97] is

\[dist_{BaulieuXI}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X|} {|X \setminus Y| + |Y \setminus X| + |(N \setminus X) \setminus Y|}\]

This is Baulieu's 29th dissimilarity coefficient. This coefficient fails Baulieu's (P4) property, that \(D(a+1,b,c,d) \leq D(a,b,c,d) = 0\) with equality holding iff \(D(a,b,c,d) = 0\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuXI} = \frac{b+c}{b+c+d}\]

New in version 0.4.0.

Initialize BaulieuXI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu XI distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu XI distance

Return type

float

Examples

>>> cmp = BaulieuXI()
>>> cmp.dist('cat', 'hat')
0.005115089514066497
>>> cmp.dist('Niall', 'Neil')
0.008951406649616368
>>> cmp.dist('aluminum', 'Catalan')
0.01913265306122449
>>> cmp.dist('ATCG', 'TAGC')
0.012755102040816327

New in version 0.4.0.

class abydos.distance.BaulieuXII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu XII distance.

For two sets X and Y and a population N, Baulieu XII distance [Bau97] is

\[dist_{BaulieuXII}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X|} {|X \cap Y| + |X \setminus Y| + |Y \setminus X| - 1}\]

This is Baulieu's 30th dissimilarity coefficient. This coefficient fails Baulieu's (P5) property, that \(D(a,b+1,c,d) \geq D(a,b,c,d)\), with equality holding if \(D(a,b,c,d) = 1\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuXII} = \frac{b+c}{a+b+c-1}\]

Notes

In the special case of comparisons where the intersection (a) contains 0 members, the size of the intersection is set to 1, resulting in a distance of 1.0. This prevents the distance from exceeding 1.0 and similarity from becoming negative.

New in version 0.4.0.

Initialize BaulieuXII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu XII distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu XII distance

Return type

float

Examples

>>> cmp = BaulieuXII()
>>> cmp.dist('cat', 'hat')
0.8
>>> cmp.dist('Niall', 'Neil')
0.875
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.BaulieuXIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu XIII distance.

For two sets X and Y and a population N, Baulieu XIII distance [Bau97] is

\[dist_{BaulieuXIII}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X|} {|X \cap Y| + |X \setminus Y| + |Y \setminus X| + |X \cap Y| \cdot (|X \cap Y| - 4)^2}\]

This is Baulieu's 31st dissimilarity coefficient. This coefficient fails Baulieu's (P4) property, that \(D(a+1,b,c,d) \leq D(a,b,c,d) = 0\) with equality holding iff \(D(a,b,c,d) = 0\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuXIII} = \frac{b+c}{a+b+c+a \cdot (a-4)^2}\]

New in version 0.4.0.

Initialize BaulieuXIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu XIII distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu XIII distance

Return type

float

Examples

>>> cmp = BaulieuXIII()
>>> cmp.dist('cat', 'hat')
0.2857142857142857
>>> cmp.dist('Niall', 'Neil')
0.4117647058823529
>>> cmp.dist('aluminum', 'Catalan')
0.6
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.BaulieuXIV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu XIV distance.

For two sets X and Y and a population N, Baulieu XIV distance [Bau97] is

\[dist_{BaulieuXIV}(X, Y) = \frac{|X \setminus Y| + 2 \cdot |Y \setminus X|}{|X \cap Y| + |X \setminus Y| + 2 \cdot |Y \setminus X|}\]

This is Baulieu's 32nd dissimilarity coefficient. This coefficient fails Baulieu's (P7) property, that \(D(a,b,c,d) = D(a,c,b,d)\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuXIV} = \frac{b+2c}{a+b+2c}\]

New in version 0.4.0.

Initialize BaulieuXIV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu XIV distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu XIV distance

Return type

float

Examples

>>> cmp = BaulieuXIV()
>>> cmp.dist('cat', 'hat')
0.75
>>> cmp.dist('Niall', 'Neil')
0.8333333333333334
>>> cmp.dist('aluminum', 'Catalan')
0.9565217391304348
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.BaulieuXV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Baulieu XV distance.

For two sets X and Y and a population N, Baulieu XV distance [Bau97] is

\[dist_{BaulieuXV}(X, Y) = \frac{|X \setminus Y| + |Y \setminus X| + max(|X \setminus Y|, |Y \setminus X|)}{|X \cap Y| + |X \setminus Y| + |Y \setminus X| + max(|X \setminus Y|, |Y \setminus X|)}\]

This is Baulieu's 33rd dissimilarity coefficient. This coefficient fails Baulieu's (P8) property, that \(D\) is a rational function whose numerator and denominator are both (total) linear.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{BaulieuXV} = \frac{b+c+max(b, c)}{a+b+c+max(b, c)}\]

New in version 0.4.0.

Initialize BaulieuXV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Baulieu XV distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Baulieu XV distance

Return type

float

Examples

>>> cmp = BaulieuXV()
>>> cmp.dist('cat', 'hat')
0.75
>>> cmp.dist('Niall', 'Neil')
0.8461538461538461
>>> cmp.dist('aluminum', 'Catalan')
0.9583333333333334
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.BeniniI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

BeniniI correlation.

For two sets X and Y and a population N, Benini I correlation, Benini's Index of Attraction, [Ben01] is

\[corr_{BeniniI}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|}{|Y| \cdot |N \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{BeniniI} = \frac{ad-bc}{(a+c)(c+d)}\]

New in version 0.4.0.

Initialize BeniniI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Benini I correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Benini I correlation

Return type

float

Examples

>>> cmp = BeniniI()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3953727506426735
>>> cmp.corr('aluminum', 'Catalan')
0.11485180412371133
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Benini I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Benini I similarity

Return type

float

Examples

>>> cmp = BeniniI()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6976863753213367
>>> cmp.sim('aluminum', 'Catalan')
0.5574259020618557
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.BeniniII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

BeniniII correlation.

For two sets X and Y and a population N, Benini II correlation, Benini's Index of Repulsion, [Ben01] is

\[corr_{BeniniII}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {min(|Y| \cdot |N \setminus X|, |X| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{BeniniII} = \frac{ad-bc}{min((a+c)(c+d), (a+b)(b+d))}\]

New in version 0.4.0.

Initialize BeniniII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Benini II correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Benini II correlation

Return type

float

Examples

>>> cmp = BeniniII()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3953727506426735
>>> cmp.corr('aluminum', 'Catalan')
0.11485180412371133
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Benini II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Benini II similarity

Return type

float

Examples

>>> cmp = BeniniII()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6976863753213367
>>> cmp.sim('aluminum', 'Catalan')
0.5574259020618557
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.Bennet(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Bennet's S correlation.

For two sets X and Y and a population N, Bennet's \(S\) correlation [BAG54] is

\[corr_{Bennet}(X, Y) = S = \frac{p_o - p_e^S}{1 - p_e^S}\]

where

\[ \begin{align}\begin{aligned}p_o = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}\\p_e^S = \frac{1}{2}\end{aligned}\end{align} \]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[ \begin{align}\begin{aligned}p_o = \frac{a+d}{n}\\p_e^S = \frac{1}{2}\end{aligned}\end{align} \]

New in version 0.4.0.

Initialize Bennet instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Bennet's S correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Bennet's S correlation

Return type

float

Examples

>>> cmp = Bennet()
>>> cmp.corr('cat', 'hat')
0.989795918367347
>>> cmp.corr('Niall', 'Neil')
0.9821428571428572
>>> cmp.corr('aluminum', 'Catalan')
0.9617834394904459
>>> cmp.corr('ATCG', 'TAGC')
0.9744897959183674

New in version 0.4.0.

sim(src, tar)[source]

Return the Bennet's S similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Bennet's S similarity

Return type

float

Examples

>>> cmp = Bennet()
>>> cmp.sim('cat', 'hat')
0.9948979591836735
>>> cmp.sim('Niall', 'Neil')
0.9910714285714286
>>> cmp.sim('aluminum', 'Catalan')
0.9808917197452229
>>> cmp.sim('ATCG', 'TAGC')
0.9872448979591837

New in version 0.4.0.

class abydos.distance.BraunBlanquet(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Braun-Blanquet similarity.

For two sets X and Y and a population N, the Braun-Blanquet similarity [BB32] is

\[sim_{BraunBlanquet}(X, Y) = \frac{|X \cap Y|}{max(|X|, |Y|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{BraunBlanquet} = \frac{a}{max(a+b, a+c)}\]

New in version 0.4.0.

Initialize BraunBlanquet instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Braun-Blanquet similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Braun-Blanquet similarity

Return type

float

Examples

>>> cmp = BraunBlanquet()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.1111111111111111
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Canberra(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Canberra distance.

For two sets X and Y, the Canberra distance [LW66][LW67b] is

\[sim_{Canberra}(X, Y) = \frac{|X \triangle Y|}{|X|+|Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Canberra} = \frac{b+c}{(a+b)+(a+c)}\]

New in version 0.4.0.

Initialize Canberra instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Canberra distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Canberra distance

Return type

float

Examples

>>> cmp = Canberra()
>>> cmp.dist('cat', 'hat')
0.5
>>> cmp.dist('Niall', 'Neil')
0.6363636363636364
>>> cmp.dist('aluminum', 'Catalan')
0.8823529411764706
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.Cao(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Cao's CY dissimilarity.

Given \(X_{ij}\) (the number of individuals of speecies \(j\) in sample \(i\)), \(X_{kj}\) (the number of individuals of speecies \(j\) in sample \(k\)), and \(N\) (the total number of speecies present in both samples), Cao dissimilarity (CYd) [CBW97] is:

\[dist_{Cao}(X, Y) = CYd = \frac{1}{N}\sum\Bigg(\frac{(X_{ij} + X_{kj})log_{10}\big( \frac{X_{ij}+X_{kj}}{2}\big)-X_{ij}log_{10}X_{kj}-X_{kj}log_{10}X_{ij}} {X_{ij}+X_{kj}}\Bigg)\]

In the above formula, whenever \(X_{ij} = 0\) or \(X_{kj} = 0\), the value 0.1 is substituted.

Since this measure ranges from 0 to \(\infty\), a similarity measure, CYs, ranging from 0 to 1 was also developed.

\[sim_{Cao}(X, Y) = CYs = 1 - \frac{Observed~CYd}{Maximum~CYd}\]

where

\[Observed~CYd = \sum\Bigg(\frac{(X_{ij} + X_{kj})log_{10}\big( \frac{X_{ij}+X_{kj}}{2}\big)-X_{ij}log_{10}X_{kj}-X_{kj}log_{10}X_{ij}} {X_{ij}+X_{kj}}\Bigg)\]

and with \(a\) (the number of species present in both samples), \(b\) (the number of species present in sample \(i\) only), and \(c\) (the number of species present in sample \(j\) only),

\[Maximum~CYd = D_1 + D_2 + D_3\]

with

\[ \begin{align}\begin{aligned}D_1 = \sum_{j=1}^b \Bigg(\frac{(X_{ij} + 0.1) log_{10} \big( \frac{X_{ij}+0.1}{2}\big)-X_{ij}log_{10}0.1-0.1log_{10}X_{ij}} {X_{ij}+0.1}\Bigg)\\D_2 = \sum_{j=1}^c \Bigg(\frac{(X_{kj} + 0.1) log_{10} \big( \frac{X_{kj}+0.1}{2}\big)-X_{kj}log_{10}0.1-0.1log_{10}X_{kj}} {X_{kj}+0.1}\Bigg)\\D_1 = \sum_{j=1}^a \frac{a}{2} \Bigg(\frac{(D_i + 1) log_{10} \big(\frac{D_i+1}{2}\big)-log_{10}D_i}{D_i+1} + \frac{(D_k + 1) log_{10} \big(\frac{D_k+1}{2}\big)-log_{10}D_k}{D_k+1}\Bigg)\end{aligned}\end{align} \]

with

\[ \begin{align}\begin{aligned}D_i = \frac{\sum X_{ij} - \frac{a}{2}}{\frac{a}{2}}\\D_k = \frac{\sum X_{kj} - \frac{a}{2}}{\frac{a}{2}}\end{aligned}\end{align} \]

for

\[ \begin{align}\begin{aligned}X_{ij} \geq 1\\X_{kj} \geq 1\end{aligned}\end{align} \]

New in version 0.4.1.

Initialize Cao instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist_abs(src, tar)[source]

Return Cao's CY dissimilarity (CYd) of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Cao's CY dissimilarity

Return type

float

Examples

>>> cmp = Cao()
>>> cmp.dist_abs('cat', 'hat')
0.3247267992925765
>>> cmp.dist_abs('Niall', 'Neil')
0.4132886536450973
>>> cmp.dist_abs('aluminum', 'Catalan')
0.5530666041976232
>>> cmp.dist_abs('ATCG', 'TAGC')
0.6494535985851531

New in version 0.4.1.

sim(src, tar)[source]

Return Cao's CY similarity (CYs) of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Cao's CY similarity

Return type

float

Examples

>>> cmp = Cao()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.1.

class abydos.distance.ChaoDice(**kwargs)[source]

Bases: abydos.distance._chao_jaccard.ChaoJaccard

Chao's Dice similarity.

Chao's Dice similarity [CCCS04]

New in version 0.4.1.

Initialize ChaoDice instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

sim(src, tar)[source]

Return the normalized Chao's Dice similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Chao's Dice similarity

Return type

float

Examples

>>> import random
>>> random.seed(0)
>>> cmp = ChaoDice()
>>> cmp.sim('cat', 'hat')
0.36666666666666664
>>> cmp.sim('Niall', 'Neil')
0.27868852459016397
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.1.

sim_score(src, tar)[source]

Return the Chao's Dice similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Chao's Dice similarity

Return type

float

Examples

>>> import random
>>> random.seed(0)
>>> cmp = ChaoDice()
>>> cmp.sim_score('cat', 'hat')
0.36666666666666664
>>> cmp.sim_score('Niall', 'Neil')
0.27868852459016397
>>> cmp.sim_score('aluminum', 'Catalan')
0.0
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.1.

class abydos.distance.ChaoJaccard(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Chao's Jaccard similarity.

Chao's Jaccard similarity [CCCS04]

New in version 0.4.1.

Initialize ChaoJaccard instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

sim(src, tar)[source]

Return normalized Chao's Jaccard similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Chao's Jaccard similarity

Return type

float

Examples

>>> import random
>>> random.seed(0)
>>> cmp = ChaoJaccard()
>>> cmp.sim('cat', 'hat')
0.22448979591836735
>>> cmp.sim('Niall', 'Neil')
0.1619047619047619
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.1.

sim_score(src, tar)[source]

Return Chao's Jaccard similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Chao's Jaccard similarity

Return type

float

Examples

>>> import random
>>> random.seed(0)
>>> cmp = ChaoJaccard()
>>> cmp.sim_score('cat', 'hat')
0.22448979591836735
>>> cmp.sim_score('Niall', 'Neil')
0.1619047619047619
>>> cmp.sim_score('aluminum', 'Catalan')
0.0
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.1.

class abydos.distance.Chebyshev(alphabet=0, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._minkowski.Minkowski

Chebyshev distance.

Euclidean distance is the chessboard distance, equivalent to Minkowski distance in \(L^\infty\)-space.

New in version 0.3.6.

Initialize Euclidean instance.

Parameters
  • alphabet (collection or int) -- The values or size of the alphabet

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Chebyshev distance

New in version 0.3.6.

dist_abs(src, tar)[source]

Return the Chebyshev distance between two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

The Chebyshev distance

Return type

float

Examples

>>> cmp = Chebyshev()
>>> cmp.dist_abs('cat', 'hat')
1.0
>>> cmp.dist_abs('Niall', 'Neil')
1.0
>>> cmp.dist_abs('Colin', 'Cuilen')
1.0
>>> cmp.dist_abs('ATCG', 'TAGC')
1.0
>>> cmp = Chebyshev(qval=1)
>>> cmp.dist_abs('ATCG', 'TAGC')
0.0
>>> cmp.dist_abs('ATCGATTCGGAATTTC', 'TAGCATAATCGCCG')
3.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

sim(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Chebyshev distance

New in version 0.3.6.

abydos.distance.chebyshev(src, tar, qval=2, alphabet=0)[source]

Return the Chebyshev distance between two strings.

This is a wrapper for the Chebyshev.dist_abs().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The Chebyshev distance

Return type

float

Examples

>>> chebyshev('cat', 'hat')
1.0
>>> chebyshev('Niall', 'Neil')
1.0
>>> chebyshev('Colin', 'Cuilen')
1.0
>>> chebyshev('ATCG', 'TAGC')
1.0
>>> chebyshev('ATCG', 'TAGC', qval=1)
0.0
>>> chebyshev('ATCGATTCGGAATTTC', 'TAGCATAATCGCCG', qval=1)
3.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Chebyshev.dist_abs method instead.

class abydos.distance.Chord(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Chord distance.

For two sets X and Y drawn from an alphabet S, the chord distance [Orloci67] is

\[sim_{chord}(X, Y) = \sqrt{\sum_{i \in S}\Big(\frac{X_i}{\sqrt{\sum_{j \in X} X_j^2}} - \frac{Y_i}{\sqrt{\sum_{j \in Y} Y_j^2}}\Big)^2}\]

New in version 0.4.0.

Initialize Chord instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Chord distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized chord distance

Return type

float

Examples

>>> cmp = Chord()
>>> cmp.dist('cat', 'hat')
0.707106781186547
>>> cmp.dist('Niall', 'Neil')
0.796775770420944
>>> cmp.dist('aluminum', 'Catalan')
0.94519820240106
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Chord distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Chord distance

Return type

float

Examples

>>> cmp = Chord()
>>> cmp.dist_abs('cat', 'hat')
1.0
>>> cmp.dist_abs('Niall', 'Neil')
1.126811100699571
>>> cmp.dist_abs('aluminum', 'Catalan')
1.336712116966249
>>> cmp.dist_abs('ATCG', 'TAGC')
1.414213562373095

New in version 0.4.0.

class abydos.distance.Clark(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Clark's coefficient of divergence.

For two sets X and Y and a population N, Clark's coefficient of divergence [Cla52] is:

\[dist_{Clark}(X, Y) = \sqrt{\frac{\sum_{i=0}^{|N|} \big(\frac{x_i-y_i}{x_i+y_i}\big)^2}{|N|}}\]

New in version 0.4.1.

Initialize Clark instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist(src, tar)[source]

Return Clark's coefficient of divergence of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Clark's coefficient of divergence

Return type

float

Examples

>>> cmp = Clark()
>>> cmp.dist('cat', 'hat')
0.816496580927726
>>> cmp.dist('Niall', 'Neil')
0.8819171036881969
>>> cmp.dist('aluminum', 'Catalan')
0.9660917830792959
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.1.

class abydos.distance.Clement(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Clement similarity.

For two sets X and Y and a population N, Clement similarity [Cle76] is defined as

\[sim_{Clement}(X, Y) = \frac{|X \cap Y|}{|X|}\Big(1-\frac{|X|}{|N|}\Big) + \frac{|(N \setminus X) \setminus Y|}{|N \setminus X|} \Big(1-\frac{|N \setminus X|}{|N|}\Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Clement} = \frac{a}{a+b}\Big(1 - \frac{a+b}{n}\Big) + \frac{d}{c+d}\Big(1 - \frac{c+d}{n}\Big)\]

New in version 0.4.0.

Initialize Clement instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Clement similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Clement similarity

Return type

float

Examples

>>> cmp = Clement()
>>> cmp.sim('cat', 'hat')
0.5025379382522239
>>> cmp.sim('Niall', 'Neil')
0.33840586363079933
>>> cmp.sim('aluminum', 'Catalan')
0.12119877280918714
>>> cmp.sim('ATCG', 'TAGC')
0.006336616803332366

New in version 0.4.0.

class abydos.distance.CohenKappa(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Cohen's Kappa similarity.

For two sets X and Y and a population N, Cohen's kappa similarity [Coh60] is

\[sim_{Cohen_\kappa}(X, Y) = \kappa = \frac{p_o - p_e^\kappa}{1 - p_e^\kappa}\]

where

\[\begin{split}\begin{array}{l} p_o = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}\\ \\ p_e^\kappa = \frac{|X|}{|N|} \cdot \frac{|Y|}{|N|} + \frac{|N \setminus X|}{|N|} \cdot \frac{|N \setminus Y|}{|N|} \end{array}\end{split}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[\begin{split}\begin{array}{l} p_o = \frac{a+d}{n}\\ \\ p_e^\kappa = \frac{a+b}{n} \cdot \frac{a+c}{n} + \frac{c+d}{n} \cdot \frac{b+d}{n} \end{array}\end{split}\]

New in version 0.4.0.

Initialize CohenKappa instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Cohen's Kappa similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Cohen's Kappa similarity

Return type

float

Examples

>>> cmp = CohenKappa()
>>> cmp.sim('cat', 'hat')
0.9974358974358974
>>> cmp.sim('Niall', 'Neil')
0.9955041746949261
>>> cmp.sim('aluminum', 'Catalan')
0.9903412749517064
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516

New in version 0.4.0.

class abydos.distance.Cole(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Cole correlation.

For two sets X and Y and a population N, the Cole correlation [Col49] has three formulae:

  • If \(|X \cap Y| \cdot |(N \setminus X) \setminus Y| \geq |X \setminus Y| \cdot |Y \setminus Y|\) then

    \[corr_{Cole}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {(|X \cap Y| + |X \setminus Y|) \cdot (|X \setminus Y| + |(N \setminus X) \setminus Y|)}\]
  • If \(|(N \setminus X) \setminus Y| \geq |X \cap Y|\) then

    \[corr_{Cole}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {(|X \cap Y| + |X \setminus Y|) \cdot (|X \cap Y| + |Y \setminus X|)}\]
  • Otherwise

    \[corr_{Cole}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {(|X \setminus Y| + |(N \setminus X) \setminus Y|) \cdot (|Y \setminus X| + |(N \setminus X) \setminus Y|)}\]

Cole terms this measurement the Coefficient of Interspecific Association.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[\begin{split}corr_{Cole} = \left\{ \begin{array}{ll} \frac{ad-bc}{(a+b)(b+d)} & \textup{if} ~ad \geq bc \\ \\ \frac{ad-bc}{(a+b)(a+c)} & \textup{if} ~d \geq a \\ \\ \frac{ad-bc}{(b+d)(c+d)} & \textup{otherwise} \end{array} \right.\end{split}\]

New in version 0.4.0.

Initialize Cole instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Cole correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Cole correlation

Return type

float

Examples

>>> cmp = Cole()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3290543431750107
>>> cmp.corr('aluminum', 'Catalan')
0.10195910195910196
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Cole similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for similarity

  • tar (str) -- Target string (or QGrams/Counter objects) for similarity

Returns

Cole similarity

Return type

float

Examples

>>> cmp = Cole()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6645271715875054
>>> cmp.sim('aluminum', 'Catalan')
0.550979550979551
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.ConsonniTodeschiniI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Consonni & Todeschini I similarity.

For two sets X and Y and a population N, Consonni & Todeschini I similarity [CT12] is

\[sim_{ConsonniTodeschiniI}(X, Y) = \frac{log(1+|X \cap Y|+|(N \setminus X) \setminus Y|)} {log(1+|N|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{ConsonniTodeschiniI} = \frac{log(1+a+d)}{log(1+n)}\]

New in version 0.4.0.

Initialize ConsonniTodeschiniI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Consonni & Todeschini I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Consonni & Todeschini I similarity

Return type

float

Examples

>>> cmp = ConsonniTodeschiniI()
>>> cmp.sim('cat', 'hat')
0.9992336018090547
>>> cmp.sim('Niall', 'Neil')
0.998656222829757
>>> cmp.sim('aluminum', 'Catalan')
0.9971098629456009
>>> cmp.sim('ATCG', 'TAGC')
0.9980766131469967

New in version 0.4.0.

class abydos.distance.ConsonniTodeschiniII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Consonni & Todeschini II similarity.

For two sets X and Y and a population N, Consonni & Todeschini II similarity [CT12] is

\[sim_{ConsonniTodeschiniII}(X, Y) = \frac{log(1+|N|) - log(1+|X \setminus Y|+|Y \setminus X|} {log(1+|N|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{ConsonniTodeschiniII} = \frac{log(1+n)-log(1+b+c)}{log(1+n)}\]

New in version 0.4.0.

Initialize ConsonniTodeschiniII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Consonni & Todeschini II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Consonni & Todeschini II similarity

Return type

float

Examples

>>> cmp = ConsonniTodeschiniII()
>>> cmp.sim('cat', 'hat')
0.7585487129939101
>>> cmp.sim('Niall', 'Neil')
0.6880377723094788
>>> cmp.sim('aluminum', 'Catalan')
0.5841297898633079
>>> cmp.sim('ATCG', 'TAGC')
0.640262668568961

New in version 0.4.0.

class abydos.distance.ConsonniTodeschiniIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Consonni & Todeschini III similarity.

For two sets X and Y and a population N, Consonni & Todeschini III similarity [CT12] is

\[sim_{ConsonniTodeschiniIII}(X, Y) = \frac{log(1+|X \cap Y|)}{log(1+|N|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{ConsonniTodeschiniIII} = \frac{log(1+a)}{log(1+n)}\]

New in version 0.4.0.

Initialize ConsonniTodeschiniIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Consonni & Todeschini III similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Consonni & Todeschini III similarity

Return type

float

Examples

>>> cmp = ConsonniTodeschiniIII()
>>> cmp.sim('cat', 'hat')
0.1648161441769704
>>> cmp.sim('Niall', 'Neil')
0.1648161441769704
>>> cmp.sim('aluminum', 'Catalan')
0.10396755253417303
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.ConsonniTodeschiniIV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Consonni & Todeschini IV similarity.

For two sets X and Y and a population N, Consonni & Todeschini IV similarity [CT12] is

\[sim_{ConsonniTodeschiniIV}(X, Y) = \frac{log(1+|X \cap Y|)}{log(1+|X \cup Y|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{ConsonniTodeschiniIV} = \frac{log(1+a)}{log(1+a+b+c)}\]

New in version 0.4.0.

Initialize ConsonniTodeschiniIV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Consonni & Todeschini IV similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Consonni & Todeschini IV similarity

Return type

float

Examples

>>> cmp = ConsonniTodeschiniIV()
>>> cmp.sim('cat', 'hat')
0.5645750340535796
>>> cmp.sim('Niall', 'Neil')
0.4771212547196623
>>> cmp.sim('aluminum', 'Catalan')
0.244650542118226
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.ConsonniTodeschiniV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Consonni & Todeschini V correlation.

For two sets X and Y and a population N, Consonni & Todeschini V correlation [CT12] is

\[corr_{ConsonniTodeschiniV}(X, Y) = \frac{log(1+|X \cap Y| \cdot |(N \setminus X) \setminus Y|)- log(1+|X \setminus Y| \cdot |Y \setminus X|)} {log(1+\frac{|N|^2}{4})}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{ConsonniTodeschiniV} = \frac{log(1+ad)-log(1+bc)}{log(1+\frac{n^2}{4})}\]

New in version 0.4.0.

Initialize ConsonniTodeschiniV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Consonni & Todeschini V correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Consonni & Todeschini V correlation

Return type

float

Examples

>>> cmp = ConsonniTodeschiniV()
>>> cmp.corr('cat', 'hat')
0.48072545510682463
>>> cmp.corr('Niall', 'Neil')
0.4003930264973547
>>> cmp.corr('aluminum', 'Catalan')
0.21794239483504532
>>> cmp.corr('ATCG', 'TAGC')
-0.2728145951429799

New in version 0.4.0.

sim(src, tar)[source]

Return the Consonni & Todeschini V similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Consonni & Todeschini V similarity

Return type

float

Examples

>>> cmp = ConsonniTodeschiniV()
>>> cmp.sim('cat', 'hat')
0.7403627275534124
>>> cmp.sim('Niall', 'Neil')
0.7001965132486774
>>> cmp.sim('aluminum', 'Catalan')
0.6089711974175227
>>> cmp.sim('ATCG', 'TAGC')
0.36359270242851005

New in version 0.4.0.

class abydos.distance.Cosine(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Cosine similarity.

For two sets X and Y, the cosine similarity, Otsuka-Ochiai coefficient, or Ochiai coefficient [Ots36][Och57] is

\[sim_{cosine}(X, Y) = \frac{|X \cap Y|}{\sqrt{|X| \cdot |Y|}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{cosine} = \frac{a}{\sqrt{(a+b)(a+c)}}\]

Notes

This measure is also known as the Fowlkes-Mallows index [FM83] for two classes and G-measure, the geometric mean of precision & recall.

New in version 0.3.6.

Initialize Cosine instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the cosine similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Cosine similarity

Return type

float

Examples

>>> cmp = Cosine()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3651483716701107
>>> cmp.sim('aluminum', 'Catalan')
0.11785113019775793
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_cosine(src, tar, qval=2)[source]

Return the cosine distance between two strings.

This is a wrapper for Cosine.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Cosine distance

Return type

float

Examples

>>> dist_cosine('cat', 'hat')
0.5
>>> dist_cosine('Niall', 'Neil')
0.6348516283298893
>>> dist_cosine('aluminum', 'Catalan')
0.882148869802242
>>> dist_cosine('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Cosine.dist method instead.

abydos.distance.sim_cosine(src, tar, qval=2)[source]

Return the cosine similarity of two strings.

This is a wrapper for Cosine.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Cosine similarity

Return type

float

Examples

>>> sim_cosine('cat', 'hat')
0.5
>>> sim_cosine('Niall', 'Neil')
0.3651483716701107
>>> sim_cosine('aluminum', 'Catalan')
0.11785113019775793
>>> sim_cosine('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Cosine.sim method instead.

class abydos.distance.Dennis(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Dennis similarity.

For two sets X and Y and a population N, Dennis similarity [Den65] is

\[sim_{Dennis}(X, Y) = \frac{|X \cap Y| - \frac{|X| \cdot |Y|}{|N|}} {\sqrt{\frac{|X|\cdot|Y|}{|N|}}}\]

This is the fourth of Dennis' association measures, and that which she claims is the best of the four.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Dennis} = \frac{a-\frac{(a+b)(a+c)}{n}}{\sqrt{\frac{(a+b)(a+c)}{n}}}\]

New in version 0.4.0.

Initialize Dennis instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Dennis correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dennis correlation

Return type

float

Examples

>>> cmp = Dennis()
>>> cmp.corr('cat', 'hat')
0.494897959183673
>>> cmp.corr('Niall', 'Neil')
0.358162114559075
>>> cmp.corr('aluminum', 'Catalan')
0.107041854561785
>>> cmp.corr('ATCG', 'TAGC')
-0.006377551020408

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Dennis similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Dennis similarity

Return type

float

Examples

>>> cmp = Dennis()
>>> cmp.sim('cat', 'hat')
0.6632653061224487
>>> cmp.sim('Niall', 'Neil')
0.5721080763727167
>>> cmp.sim('aluminum', 'Catalan')
0.4046945697078567
>>> cmp.sim('ATCG', 'TAGC')
0.32908163265306134

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Dennis similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dennis similarity

Return type

float

Examples

>>> cmp = Dennis()
>>> cmp.sim_score('cat', 'hat')
13.857142857142858
>>> cmp.sim_score('Niall', 'Neil')
10.028539207654113
>>> cmp.sim_score('aluminum', 'Catalan')
2.9990827802847835
>>> cmp.sim_score('ATCG', 'TAGC')
-0.17857142857142858

New in version 0.4.0.

class abydos.distance.Dice(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._tversky.Tversky

Sørensen–Dice coefficient.

For two sets X and Y, the Sørensen–Dice coefficient [Dic45][Sorensen48][Cze09][MDobrzanskiZ50] is

\[sim_{Dice}(X, Y) = \frac{2 \cdot |X \cap Y|}{|X| + |Y|}\]

This is the complement of Bray & Curtis dissimilarity [BC57], also known as the Lance & Williams dissimilarity [LW67a].

This is identical to the Tanimoto similarity coefficient [Tan58] and the Tversky index [Tve77] for \(\alpha = \beta = 0.5\).

In the Ruby text library this is identified as White similarity, after [Whid.].

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Dice} = \frac{2a}{2a+b+c}\]

Notes

In terms of a confusion matrix, this is equivalent to \(F_1\) score ConfusionTable.f1_score().

The multiset variant is termed Gleason similarity [Gle20].

New in version 0.3.6.

Initialize Dice instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sørensen–Dice coefficient of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sørensen–Dice similarity

Return type

float

Examples

>>> cmp = Dice()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.11764705882352941
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_dice(src, tar, qval=2)[source]

Return the Sørensen–Dice distance between two strings.

This is a wrapper for Dice.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Sørensen–Dice distance

Return type

float

Examples

>>> dist_dice('cat', 'hat')
0.5
>>> dist_dice('Niall', 'Neil')
0.6363636363636364
>>> dist_dice('aluminum', 'Catalan')
0.8823529411764706
>>> dist_dice('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Dice.dist method instead.

abydos.distance.sim_dice(src, tar, qval=2)[source]

Return the Sørensen–Dice coefficient of two strings.

This is a wrapper for Dice.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Sørensen–Dice similarity

Return type

float

Examples

>>> sim_dice('cat', 'hat')
0.5
>>> sim_dice('Niall', 'Neil')
0.36363636363636365
>>> sim_dice('aluminum', 'Catalan')
0.11764705882352941
>>> sim_dice('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Dice.sim method instead.

class abydos.distance.DiceAsymmetricI(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Dice's Asymmetric I similarity.

For two sets X and Y and a population N, Dice's Asymmetric I similarity [Dic45] is

\[sim_{DiceAsymmetricI}(X, Y) = \frac{|X \cap Y|}{|X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{DiceAsymmetricI} = \frac{a}{a+b}\]

Notes

In terms of a confusion matrix, this is equivalent to precision or positive predictive value ConfusionTable.precision().

New in version 0.4.0.

Initialize DiceAsymmetricI instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Dice's Asymmetric I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dice's Asymmetric I similarity

Return type

float

Examples

>>> cmp = DiceAsymmetricI()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.1111111111111111
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.DiceAsymmetricII(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Dice's Asymmetric II similarity.

For two sets X and Y, Dice's Asymmetric II similarity [Dic45] is

\[sim_{DiceAsymmetricII}(X, Y) = \frac{|X \cap Y|}{|Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{DiceAsymmetricII} = \frac{a}{a+c}\]

Notes

In terms of a confusion matrix, this is equivalent to recall, sensitivity, or true positive rate ConfusionTable.recall().

New in version 0.4.0.

Initialize DiceAsymmetricII instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Dice's Asymmetric II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dice's Asymmetric II similarity

Return type

float

Examples

>>> cmp = DiceAsymmetricII()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.4
>>> cmp.sim('aluminum', 'Catalan')
0.125
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Digby(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Digby correlation.

For two sets X and Y and a population N, Digby's approximation of the tetrachoric correlation coefficient [Dig83] is

\[corr_{Digby}(X, Y) = \frac{(|X \cap Y| \cdot |(N \setminus X) \setminus Y|)^\frac{3}{4}- (|X \setminus Y| \cdot |Y \setminus X|)^\frac{3}{4}} {(|X \cap Y| \cdot |(N \setminus X) \setminus Y|)^\frac{3}{4} + (|X \setminus Y| \cdot |Y \setminus X|)^\frac{3}{4}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Digby} = \frac{ad^\frac{3}{4}-bc^\frac{3}{4}}{ad^\frac{3}{4}+bc^\frac{3}{4}}\]

New in version 0.4.0.

Initialize Digby instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Digby correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Digby correlation

Return type

float

Examples

>>> cmp = Digby()
>>> cmp.corr('cat', 'hat')
0.9774244829419212
>>> cmp.corr('Niall', 'Neil')
0.9491281473458171
>>> cmp.corr('aluminum', 'Catalan')
0.7541039303781305
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Digby similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Digby similarity

Return type

float

Examples

>>> cmp = Digby()
>>> cmp.sim('cat', 'hat')
0.9887122414709606
>>> cmp.sim('Niall', 'Neil')
0.9745640736729085
>>> cmp.sim('aluminum', 'Catalan')
0.8770519651890653
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Dispersion(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Dispersion correlation.

For two sets X and Y and a population N, the dispersion correlation [Cor17] is

\[corr_{dispersion}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {|N|^2}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{dispersion} = \frac{ad-bc}{n^2}\]

New in version 0.4.0.

Initialize Dispersion instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Dispersion correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dispersion correlation

Return type

float

Examples

>>> cmp = Dispersion()
>>> cmp.corr('cat', 'hat')
0.002524989587671803
>>> cmp.corr('Niall', 'Neil')
0.002502212619741774
>>> cmp.corr('aluminum', 'Catalan')
0.0011570449105440383
>>> cmp.corr('ATCG', 'TAGC')
-4.06731570179092e-05

New in version 0.4.0.

sim(src, tar)[source]

Return the Dispersion similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dispersion similarity

Return type

float

Examples

>>> cmp = Dispersion()
>>> cmp.sim('cat', 'hat')
0.5012624947938359
>>> cmp.sim('Niall', 'Neil')
0.5012511063098709
>>> cmp.sim('aluminum', 'Catalan')
0.500578522455272
>>> cmp.sim('ATCG', 'TAGC')
0.499979663421491

New in version 0.4.0.

class abydos.distance.Doolittle(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Doolittle similarity.

For two sets X and Y and a population N, the Doolittle similarity [Doo84] is

\[sim_{Doolittle}(X, Y) = \frac{(|X \cap Y| \cdot |N| - |X| \cdot |Y|)^2} {|X| \cdot |Y| \cdot |N \setminus Y| \cdot |N \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Doolittle} = \frac{(an-(a+b)(a+c))^2}{(a+b)(a+c)(b+d)(c+d)}\]

New in version 0.4.0.

Initialize Doolittle instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Doolittle similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Doolittle similarity

Return type

float

Examples

>>> cmp = Doolittle()
>>> cmp.sim('cat', 'hat')
0.24744247205785666
>>> cmp.sim('Niall', 'Neil')
0.13009912077202224
>>> cmp.sim('aluminum', 'Catalan')
0.011710186806836291
>>> cmp.sim('ATCG', 'TAGC')
4.1196952743799446e-05

New in version 0.4.0.

class abydos.distance.Dunning(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Dunning similarity.

For two sets X and Y and a population N, Dunning log-likelihood [Dun93], following [CGHH91], is

\[\begin{split}sim_{Dunning}(X, Y) = \lambda = |X \cap Y| \cdot log_2(|X \cap Y|) +\\ |X \setminus Y| \cdot log_2(|X \setminus Y|) + |Y \setminus X| \cdot log_2(|Y \setminus X|) +\\ |(N \setminus X) \setminus Y| \cdot log_2(|(N \setminus X) \setminus Y|) -\\ (|X| \cdot log_2(|X|) + |Y| \cdot log_2(|Y|) +\\ |N \setminus Y| \cdot log_2(|N \setminus Y|) + |N \setminus X| \cdot log_2(|N \setminus X|))\end{split}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[\begin{split}sim_{Dunning} = \lambda = a \cdot log_2(a) +\\ b \cdot log_2(b) + c \cdot log_2(c) + d \cdot log_2(d) - \\ ((a+b) \cdot log_2(a+b) + (a+c) \cdot log_2(a+c) +\\ (b+d) \cdot log_2(b+d) + (c+d) log_2(c+d))\end{split}\]

Notes

To avoid NaNs, every logarithm is calculated as the logarithm of 1 greater than the value in question. (Python's math.log1p function is used.)

New in version 0.4.0.

Initialize Dunning instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Dunning similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Dunning similarity

Return type

float

Examples

>>> cmp = Dunning()
>>> cmp.sim('cat', 'hat')
0.33462839191969423
>>> cmp.sim('Niall', 'Neil')
0.19229445539929793
>>> cmp.sim('aluminum', 'Catalan')
0.03220862737070572
>>> cmp.sim('ATCG', 'TAGC')
0.0010606026735052122

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Dunning similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Dunning similarity

Return type

float

Examples

>>> cmp = Dunning()
>>> cmp.sim('cat', 'hat')
0.33462839191969423
>>> cmp.sim('Niall', 'Neil')
0.19229445539929793
>>> cmp.sim('aluminum', 'Catalan')
0.03220862737070572
>>> cmp.sim('ATCG', 'TAGC')
0.0010606026735052122

New in version 0.4.0.

class abydos.distance.Euclidean(alphabet=0, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._minkowski.Minkowski

Euclidean distance.

Euclidean distance is the straigh-line or as-the-crow-flies distance, equivalent to Minkowski distance in \(L^2\)-space.

New in version 0.3.6.

Initialize Euclidean instance.

Parameters
  • alphabet (collection or int) -- The values or size of the alphabet

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Euclidean distance between two strings.

The normalized Euclidean distance is a distance metric in \(L^2\)-space, normalized to [0, 1].

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

The normalized Euclidean distance

Return type

float

Examples

>>> cmp = Euclidean()
>>> round(cmp.dist('cat', 'hat'), 12)
0.57735026919
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.683130051064
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.727606875109
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar, normalized=False)[source]

Return the Euclidean distance between two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • normalized (bool) -- Normalizes to [0, 1] if True

Returns

The Euclidean distance

Return type

float

Examples

>>> cmp = Euclidean()
>>> cmp.dist_abs('cat', 'hat')
2.0
>>> round(cmp.dist_abs('Niall', 'Neil'), 12)
2.645751311065
>>> cmp.dist_abs('Colin', 'Cuilen')
3.0
>>> round(cmp.dist_abs('ATCG', 'TAGC'), 12)
3.162277660168

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.euclidean(src, tar, qval=2, normalized=False, alphabet=0)[source]

Return the Euclidean distance between two strings.

This is a wrapper for Euclidean.dist_abs().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • normalized (bool) -- Normalizes to [0, 1] if True

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

float

Return type

The Euclidean distance

Examples

>>> euclidean('cat', 'hat')
2.0
>>> round(euclidean('Niall', 'Neil'), 12)
2.645751311065
>>> euclidean('Colin', 'Cuilen')
3.0
>>> round(euclidean('ATCG', 'TAGC'), 12)
3.162277660168

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Euclidean.dist_abs method instead.

abydos.distance.dist_euclidean(src, tar, qval=2, alphabet=0)[source]

Return the normalized Euclidean distance between two strings.

This is a wrapper for Euclidean.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The normalized Euclidean distance

Return type

float

Examples

>>> round(dist_euclidean('cat', 'hat'), 12)
0.57735026919
>>> round(dist_euclidean('Niall', 'Neil'), 12)
0.683130051064
>>> round(dist_euclidean('Colin', 'Cuilen'), 12)
0.727606875109
>>> dist_euclidean('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Euclidean.dist method instead.

abydos.distance.sim_euclidean(src, tar, qval=2, alphabet=0)[source]

Return the normalized Euclidean similarity of two strings.

This is a wrapper for Euclidean.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The normalized Euclidean similarity

Return type

float

Examples

>>> round(sim_euclidean('cat', 'hat'), 12)
0.42264973081
>>> round(sim_euclidean('Niall', 'Neil'), 12)
0.316869948936
>>> round(sim_euclidean('Colin', 'Cuilen'), 12)
0.272393124891
>>> sim_euclidean('ATCG', 'TAGC')
0.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Euclidean.sim method instead.

class abydos.distance.Eyraud(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Eyraud similarity.

For two sets X and Y and a population N, the Eyraud similarity [Eyr38] is

\[sim_{Eyraud}(X, Y) = \frac{|X \cap Y| - |X| \cdot |Y|} {|X| \cdot |Y| \cdot |N \setminus Y| \cdot |N \setminus X|}\]

For lack of access to the original, this formula is based on the concurring formulae presented in [Shi93] and [Hubalek08].

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Eyraud} = \frac{a-(a+b)(a+c)}{(a+b)(a+c)(b+d)(c+d)}\]

New in version 0.4.0.

Initialize Eyraud instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Eyraud similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Eyraud similarity

Return type

float

Examples

>>> cmp = Eyraud()
>>> cmp.sim('cat', 'hat')
1.438198553583169e-06
>>> cmp.sim('Niall', 'Neil')
1.5399964580081465e-06
>>> cmp.sim('aluminum', 'Catalan')
1.6354719962967386e-06
>>> cmp.sim('ATCG', 'TAGC')
1.6478781097519779e-06

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Eyraud similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Eyraud similarity

Return type

float

Examples

>>> cmp = Eyraud()
>>> cmp.sim_score('cat', 'hat')
-1.438198553583169e-06
>>> cmp.sim_score('Niall', 'Neil')
-1.5399964580081465e-06
>>> cmp.sim_score('aluminum', 'Catalan')
-1.6354719962967386e-06
>>> cmp.sim_score('ATCG', 'TAGC')
-1.6478781097519779e-06

New in version 0.4.0.

class abydos.distance.FagerMcGowan(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Fager & McGowan similarity.

For two sets X and Y, the Fager & McGowan similarity [Fag57][FM63] is

\[sim_{FagerMcGowan}(X, Y) = \frac{|X \cap Y|}{\sqrt{|X|\cdot|Y|}} - \frac{1}{2\sqrt{max(|X|, |Y|)}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{FagerMcGowan} = \frac{a}{\sqrt{(a+b)(a+c)}} - \frac{1}{2\sqrt{max(a+b, a+c)}}\]

New in version 0.4.0.

Initialize FagerMcGowan instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Fager & McGowan similarity of two strings.

As this similarity ranges from \((-\inf, 1.0)\), this normalization simply clamps the value to the range (0.0, 1.0).

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Fager & McGowan similarity

Return type

float

Examples

>>> cmp = FagerMcGowan()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.16102422643817918
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Fager & McGowan similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fager & McGowan similarity

Return type

float

Examples

>>> cmp = FagerMcGowan()
>>> cmp.sim_score('cat', 'hat')
0.25
>>> cmp.sim_score('Niall', 'Neil')
0.16102422643817918
>>> cmp.sim_score('aluminum', 'Catalan')
-0.048815536468908724
>>> cmp.sim_score('ATCG', 'TAGC')
-0.22360679774997896

New in version 0.4.0.

class abydos.distance.Faith(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Faith similarity.

For two sets X and Y and a population N, the Faith similarity [Fai83] is

\[sim_{Faith}(X, Y) = \frac{|X \cap Y| + \frac{|(N \setminus X) \setminus Y|}{2}}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Faith} = \frac{a+\frac{d}{2}}{n}\]

New in version 0.4.0.

Initialize Faith instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Faith similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Faith similarity

Return type

float

Examples

>>> cmp = Faith()
>>> cmp.sim('cat', 'hat')
0.4987244897959184
>>> cmp.sim('Niall', 'Neil')
0.4968112244897959
>>> cmp.sim('aluminum', 'Catalan')
0.4910828025477707
>>> cmp.sim('ATCG', 'TAGC')
0.49362244897959184

New in version 0.4.0.

class abydos.distance.Fidelity(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Fidelity.

For two multisets X and Y drawn from an alphabet S, fidelity is

\[sim_{Fidelity}(X, Y) = \Bigg( \sum_{i \in S} \sqrt{|\frac{A_i}{|A|} \cdot \frac{B_i}{|B|}|} \Bigg)^2\]

New in version 0.4.0.

Initialize Fidelity instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the fidelity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

fidelity

Return type

float

Examples

>>> cmp = Fidelity()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.1333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.013888888888888888
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Fleiss(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Fleiss correlation.

For two sets X and Y and a population N, Fleiss correlation [Fle75] is

\[corr_{Fleiss}(X, Y) = \frac{(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|) \cdot (|X| \cdot |N \setminus X| + |Y| \cdot |N \setminus Y|)} {2 \cdot |X| \cdot |N \setminus X| \cdot |Y| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Fleiss} = \frac{(ad-bc)((a+b)(c+d)+(a+c)(b+d))}{2(a+b)(c+d)(a+c)(b+d)}\]

This is Fleiss' \(M(A_1)\), \(ad-bc\) divided by the harmonic mean of the marginals \(p_1q_1 = (a+b)(c+d)\) and \(p_2q_2 = (a+c)(b+d)\).

New in version 0.4.0.

Initialize Fleiss instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Fleiss correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fleiss correlation

Return type

float

Examples

>>> cmp = Fleiss()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3621712520061204
>>> cmp.corr('aluminum', 'Catalan')
0.10839724112919989
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Fleiss similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fleiss similarity

Return type

float

Examples

>>> cmp = Fleiss()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6810856260030602
>>> cmp.sim('aluminum', 'Catalan')
0.5541986205645999
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.FleissLevinPaik(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Fleiss-Levin-Paik similarity.

For two sets X and Y and a population N, Fleiss-Levin-Paik similarity [FLP03] is

\[sim_{FleissLevinPaik}(X, Y) = \frac{2|(N \setminus X) \setminus Y|} {2|(N \setminus X) \setminus Y| + |X \setminus Y| + |Y \setminus X|}\]

This is [Mor12]'s 'd Specific Agreement'.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{FleissLevinPaik} = \frac{2d}{2d + b + c}\]

New in version 0.4.0.

Initialize FleissLevinPaik instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Fleiss-Levin-Paik similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fleiss-Levin-Paik similarity

Return type

float

Examples

>>> cmp = FleissLevinPaik()
>>> cmp.sim('cat', 'hat')
0.9974358974358974
>>> cmp.sim('Niall', 'Neil')
0.9955041746949261
>>> cmp.sim('aluminum', 'Catalan')
0.9903412749517064
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516

New in version 0.4.0.

class abydos.distance.ForbesI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Forbes I similarity.

For two sets X and Y and a population N, the Forbes I similarity [For07][Moz36] is

\[sim_{ForbesI}(X, Y) = \frac{|N| \cdot |X \cap Y|}{|X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{ForbesI} = \frac{na}{(a+b)(a+c)}\]

New in version 0.4.0.

Initialize ForbesI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Forbes I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Forbes I similarity

Return type

float

Examples

>>> cmp = ForbesI()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.11125283446712018
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Forbes I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Forbes I similarity

Return type

float

Examples

>>> cmp = ForbesI()
>>> cmp.sim_score('cat', 'hat')
98.0
>>> cmp.sim_score('Niall', 'Neil')
52.266666666666666
>>> cmp.sim_score('aluminum', 'Catalan')
10.902777777777779
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.ForbesII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Forbes II correlation.

For two sets X and Y and a population N, the Forbes II correlation, as described in [For25], is

\[corr_{ForbesII}(X, Y) = \frac{|X \setminus Y| \cdot |Y \setminus X| - |X \cap Y| \cdot |(N \setminus X) \setminus Y|} {|X| \cdot |Y| - |N| \cdot min(|X|, |Y|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{ForbesII} = \frac{bc-ad}{(a+b)(a+c) - n \cdot min(a+b, a+c)}\]

New in version 0.4.0.

Initialize ForbesII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Forbes II correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Forbes II correlation

Return type

float

Examples

>>> cmp = ForbesII()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3953727506426735
>>> cmp.corr('aluminum', 'Catalan')
0.11485180412371133
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Forbes II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Forbes II similarity

Return type

float

Examples

>>> cmp = ForbesII()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6976863753213367
>>> cmp.sim('aluminum', 'Catalan')
0.5574259020618557
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.Fossum(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Fossum similarity.

For two sets X and Y and a population N, the Fossum similarity [FK66] is

\[sim_{Fossum}(X, Y) = \frac{|N| \cdot \Big(|X \cap Y|-\frac{1}{2}\Big)^2}{|X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Fossum} = \frac{n(a-\frac{1}{2})^2}{(a+b)(a+c)}\]

New in version 0.4.0.

Initialize Fossum instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Fossum similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Fossum similarity

Return type

float

Examples

>>> cmp = Fossum()
>>> cmp.sim('cat', 'hat')
0.1836734693877551
>>> cmp.sim('Niall', 'Neil')
0.08925619834710742
>>> cmp.sim('aluminum', 'Catalan')
0.0038927335640138415
>>> cmp.sim('ATCG', 'TAGC')
0.01234567901234568

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Fossum similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fossum similarity

Return type

float

Examples

>>> cmp = Fossum()
>>> cmp.sim_score('cat', 'hat')
110.25
>>> cmp.sim_score('Niall', 'Neil')
58.8
>>> cmp.sim_score('aluminum', 'Catalan')
2.7256944444444446
>>> cmp.sim_score('ATCG', 'TAGC')
7.84

New in version 0.4.0.

class abydos.distance.GeneralizedFleiss(alphabet=None, tokenizer=None, intersection_type='crisp', mean_func='arithmetic', marginals='a', proportional=False, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Generalized Fleiss correlation.

For two sets X and Y and a population N, Generalized Fleiss correlation is based on observations from [Fle75].

\[corr_{GeneralizedFleiss}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {\mu_{products~of~marginals}}\]

The mean function \(\mu\) may be any of the mean functions in abydos.stats. The products of marginals may be one of the following:

  • a : \(|X| \cdot |N \setminus X|\) & \(|Y| \cdot |N \setminus Y|\)

  • b : \(|X| \cdot |Y|\) & \(|N \setminus X| \cdot |N \setminus Y|\)

  • c : \(|X| \cdot |N| \setminus Y|\) & \(|Y| \cdot |N \setminus X|\)

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{GeneralizedFleiss} = \frac{ad-bc}{\mu_{products~of~marginals}}\]

And the products of marginals are:

  • a : \(p_1q_1 = (a+b)(c+d)\) & \(p_2q_2 = (a+c)(b+d)\)

  • b : \(p_1p_2 = (a+b)(a+c)\) & \(q_1q_2 = (c+d)(b+d)\)

  • c : \(p_1q_2 = (a+b)(b+d)\) & \(p_2q_1 = (a+c)(c+d)\)

New in version 0.4.0.

Initialize GeneralizedFleiss instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • mean_func (str or function) --

    Specifies the mean function to use. A function taking a list of numbers as its only required argument may be supplied, or one of the following strings will select the specified mean function from abydos.stats:

    • arithmetic employs amean(), and this measure will be identical to MaxwellPilliner with otherwise default parameters

    • geometric employs gmean(), and this measure will be identical to PearsonPhi with otherwise default parameters

    • harmonic employs hmean(), and this measure will be identical to Fleiss with otherwise default parameters

    • ag employs the arithmetic-geometric mean agmean()

    • gh employs the geometric-harmonic mean ghmean()

    • agh employs the arithmetic-geometric-harmonic mean aghmean()

    • contraharmonic employs the contraharmonic mean cmean()

    • identric employs the identric mean imean()

    • logarithmic employs the logarithmic mean lmean()

    • quadratic employs the quadratic mean qmean()

    • heronian employs the Heronian mean heronian_mean()

    • hoelder employs the Hölder mean hoelder_mean()

    • lehmer employs the Lehmer mean lehmer_mean()

    • seiffert employs Seiffert's mean seiffert_mean()

  • marginals (str) --

    Specifies the pairs of marginals to multiply and calculate the resulting mean of. Can be:

    • a : \(p_1q_1 = (a+b)(c+d)\) & \(p_2q_2 = (a+c)(b+d)\)

    • b : \(p_1p_2 = (a+b)(a+c)\) & \(q_1q_2 = (c+d)(b+d)\)

    • c : \(p_1q_2 = (a+b)(b+d)\) & \(p_2q_1 = (a+c)(c+d)\)

  • proportional (bool) -- If true, each of the values, \(a, b, c, d\) and the marginals will be divided by the total \(a+b+c+d=n\).

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Generalized Fleiss correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Generalized Fleiss correlation

Return type

float

Examples

>>> cmp = GeneralizedFleiss()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.35921989956790845
>>> cmp.corr('aluminum', 'Catalan')
0.10803030303030303
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Generalized Fleiss similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Generalized Fleiss similarity

Return type

float

Examples

>>> cmp = GeneralizedFleiss()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6796099497839543
>>> cmp.sim('aluminum', 'Catalan')
0.5540151515151515
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.Gilbert(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Gilbert correlation.

For two sets X and Y and a population N, the Gilbert correlation [Gil84] is

\[corr_{Gilbert}(X, Y) = \frac{2(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)} {|N|^2 - |X \cap Y|^2 + |X \setminus Y|^2 + |Y \setminus X|^2 - |(N \setminus X) \setminus Y|^2}\]

For lack of access to the original, this formula is based on the concurring formulae presented in [Pei84] and [Doo84].

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Gilbert} = \frac{2(ad-cd)}{n^2-a^2+b^2+c^2-d^2}\]

New in version 0.4.0.

Initialize Gilbert instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Gilbert correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gilbert correlation

Return type

float

Examples

>>> cmp = Gilbert()
>>> cmp.corr('cat', 'hat')
0.3310580204778157
>>> cmp.corr('Niall', 'Neil')
0.21890122402504983
>>> cmp.corr('aluminum', 'Catalan')
0.057094811018577836
>>> cmp.corr('ATCG', 'TAGC')
-0.003198976327575176

New in version 0.4.0.

sim(src, tar)[source]

Return the Gilbert similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gilbert similarity

Return type

float

Examples

>>> cmp = Gilbert()
>>> cmp.sim('cat', 'hat')
0.6655290102389079
>>> cmp.sim('Niall', 'Neil')
0.6094506120125249
>>> cmp.sim('aluminum', 'Catalan')
0.5285474055092889
>>> cmp.sim('ATCG', 'TAGC')
0.4984005118362124

New in version 0.4.0.

class abydos.distance.GilbertWells(alphabet=None, tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Gilbert & Wells similarity.

For two sets X and Y and a population N, the Gilbert & Wells similarity [GW66] is

\[sim_{GilbertWells}(X, Y) = ln \frac{|N|^3}{2\pi |X| \cdot |Y| \cdot |N \setminus Y| \cdot |N \setminus X|} + 2ln \frac{|N|! \cdot |X \cap Y|! \cdot |X \setminus Y|! \cdot |Y \setminus X|! \cdot |(N \setminus X) \setminus Y|!} {|X|! \cdot |Y|! \cdot |N \setminus Y|! \cdot |N \setminus X|!}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{GilbertWells} = ln \frac{n^3}{2\pi (a+b)(a+c)(b+d)(c+d)} + 2ln \frac{n!a!b!c!d!}{(a+b)!(a+c)!(b+d)!(c+d)!}\]

Notes

Most lists of similarity & distance measures, including [Hubalek08][CCT10][Mor12] have a quite different formula, which would be \(ln~a - ln~b - ln \frac{a+b}{n} - ln \frac{a+c}{n} = ln\frac{an}{(a+b)(a+c)}\). However, neither this formula nor anything similar or equivalent to it appears anywhere within the cited work, [GW66]. See :class:UnknownF for this, alternative, measure.

New in version 0.4.0.

Initialize GilbertWells instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Gilbert & Wells similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Gilbert & Wells similarity

Return type

float

Examples

>>> cmp = GilbertWells()
>>> cmp.sim('cat', 'hat')
0.4116913723876516
>>> cmp.sim('Niall', 'Neil')
0.2457247406857589
>>> cmp.sim('aluminum', 'Catalan')
0.05800001636414742
>>> cmp.sim('ATCG', 'TAGC')
0.028716013247135602

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Gilbert & Wells similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gilbert & Wells similarity

Return type

float

Examples

>>> cmp = GilbertWells()
>>> cmp.sim_score('cat', 'hat')
20.17617447734673
>>> cmp.sim_score('Niall', 'Neil')
16.717742356982733
>>> cmp.sim_score('aluminum', 'Catalan')
5.495096667524002
>>> cmp.sim_score('ATCG', 'TAGC')
1.6845961909440712

New in version 0.4.0.

class abydos.distance.GiniI(alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Gini I correlation.

For two sets X and Y and a population N, Gini I correlation [Gin12], using the formula from [GK59], is

\[corr_{GiniI}(X, Y) = \frac{\frac{|X \cap Y|+|(N \setminus X) \setminus Y|}{|N|} - \frac{|X| \cdot |Y|}{|N|} + \frac{|N \setminus Y| \cdot |N \setminus X|}{|N|}} {\sqrt{(1-(\frac{|X|}{|N|}^2+\frac{|Y|}{|N|}^2)) \cdot (1-(\frac{|N \setminus Y|}{|N|}^2 + \frac{|N \setminus X|}{|N|}^2))}}\]

In 2x2 confusion table terms, where a+b+c+d=n, after each term has been converted to a proportion by dividing by n, this is

\[corr_{GiniI} = \frac{(a+d)-(a+b)(a+c) + (b+d)(c+d)} {\sqrt{(1-((a+b)^2+(c+d)^2))\cdot(1-((a+c)^2+(b+d)^2))}}\]

New in version 0.4.0.

Initialize GiniI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • normalizer (str) -- Specifies the normalization type. See normalizer description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Gini I correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gini I correlation

Return type

float

Examples

>>> cmp = GiniI()
>>> cmp.corr('cat', 'hat')
0.49722814498933254
>>> cmp.corr('Niall', 'Neil')
0.39649090262533215
>>> cmp.corr('aluminum', 'Catalan')
0.14887105223941113
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237489576

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Gini I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Gini I similarity

Return type

float

Examples

>>> cmp = GiniI()
>>> cmp.sim('cat', 'hat')
0.7486140724946663
>>> cmp.sim('Niall', 'Neil')
0.6982454513126661
>>> cmp.sim('aluminum', 'Catalan')
0.5744355261197056
>>> cmp.sim('ATCG', 'TAGC')
0.4967907573812552

New in version 0.4.0.

class abydos.distance.GiniII(alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Gini II distance.

For two sets X and Y and a population N, Gini II correlation [Gin15], using the formula from [GK59], is

\[corr_{GiniII}(X, Y) = \frac{\frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|} - (\frac{|X| \cdot |Y|}{|N|} + \frac{|N \setminus Y| \cdot |N \setminus X|}{|N|})} {1 - |\frac{|Y \setminus X| - |X \setminus Y|}{|N|}| - (\frac{|X| \cdot |Y|}{|N|} + \frac{|N \setminus Y| \cdot |N \setminus X|}{|N|})}\]

In 2x2 confusion table terms, where a+b+c+d=n, after each term has been converted to a proportion by dividing by n, this is

\[corr_{GiniII} = \frac{(a+d) - ((a+b)(a+c) + (b+d)(c+d))} {1 - |b-c| - ((a+b)(a+c) + (b+d)(c+d))}\]

New in version 0.4.0.

Initialize GiniII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • normalizer (str) -- Specifies the normalization type. See normalizer description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Gini II correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gini II correlation

Return type

float

Examples

>>> cmp = GiniII()
>>> cmp.corr('cat', 'hat')
0.49722814498933254
>>> cmp.corr('Niall', 'Neil')
0.4240703425535771
>>> cmp.corr('aluminum', 'Catalan')
0.15701415701415936
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237489576

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Gini II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Gini II similarity

Return type

float

Examples

>>> cmp = GiniII()
>>> cmp.sim('cat', 'hat')
0.7486140724946663
>>> cmp.sim('Niall', 'Neil')
0.7120351712767885
>>> cmp.sim('aluminum', 'Catalan')
0.5785070785070797
>>> cmp.sim('ATCG', 'TAGC')
0.4967907573812552

New in version 0.4.0.

class abydos.distance.Goodall(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Goodall similarity.

For two sets X and Y and a population N, Goodall similarity [Goo67][AC77] is an angular transformation of Sokal & Michener's simple matching coefficient

\[sim_{Goodall}(X, Y) = \frac{2}{\pi} \sin^{-1}\Big( \sqrt{\frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}} \Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Goodall} =\frac{2}{\pi} \sin^{-1}\Big( \sqrt{\frac{a + d}{n}} \Big)\]

New in version 0.4.0.

Initialize Goodall instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Goodall similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Goodall similarity

Return type

float

Examples

>>> cmp = Goodall()
>>> cmp.sim('cat', 'hat')
0.9544884026871964
>>> cmp.sim('Niall', 'Neil')
0.9397552079794624
>>> cmp.sim('aluminum', 'Catalan')
0.9117156301536503
>>> cmp.sim('ATCG', 'TAGC')
0.9279473952929225

New in version 0.4.0.

class abydos.distance.GoodmanKruskalLambda(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Goodman & Kruskal's Lambda similarity.

For two sets X and Y and a population N, Goodman & Kruskal's lambda [GK54] is

\[sim_{GK_\lambda}(X, Y) = \frac{\frac{1}{2}(max(|X \cap Y|, |X \setminus Y|)+ max(|Y \setminus X|, |(N \setminus X) \setminus Y|)+ max(|X \cap Y|, |Y \setminus X|)+ max(|X \setminus Y|, |(N \setminus X) \setminus Y|))- (max(|X|, |N \setminus X|)+max(|Y|, |N \setminus Y|))} {|N|-\frac{1}{2}(max(|X|, |N \setminus X|)+ max(|Y|, |N \setminus Y|))}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{GK_\lambda} = \frac{\frac{1}{2}((max(a,b)+max(c,d)+max(a,c)+max(b,d))- (max(a+b,c+d)+max(a+c,b+d)))} {n-\frac{1}{2}(max(a+b,c+d)+max(a+c,b+d))}\]

New in version 0.4.0.

Initialize GoodmanKruskalLambda instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Goodman & Kruskal's Lambda similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Goodman & Kruskal's Lambda similarity

Return type

float

Examples

>>> cmp = GoodmanKruskalLambda()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.GoodmanKruskalLambdaR(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Goodman & Kruskal Lambda-r correlation.

For two sets X and Y and a population N, Goodman & Kruskal \(\lambda_r\) correlation [GK54] is

\[corr_{GK_{\lambda_r}}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y| - \frac{1}{2}(max(|X|, |N \setminus X|) + max(|Y|, |N \setminus Y|))} {|N| - \frac{1}{2}(max(|X|, |N \setminus X|) + max(|Y|, |N \setminus Y|))}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{GK_{\lambda_r}} = \frac{a + d - \frac{1}{2}(max(a+b,c+d)+max(a+c,b+d))} {n - \frac{1}{2}(max(a+b,c+d)+max(a+c,b+d))}\]

New in version 0.4.0.

Initialize GoodmanKruskalLambdaR instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return Goodman & Kruskal Lambda-r correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Goodman & Kruskal Lambda-r correlation

Return type

float

Examples

>>> cmp = GoodmanKruskalLambdaR()
>>> cmp.corr('cat', 'hat')
0.0
>>> cmp.corr('Niall', 'Neil')
-0.2727272727272727
>>> cmp.corr('aluminum', 'Catalan')
-0.7647058823529411
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return Goodman & Kruskal Lambda-r similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Goodman & Kruskal Lambda-r similarity

Return type

float

Examples

>>> cmp = GoodmanKruskalLambdaR()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.11764705882352944
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.GoodmanKruskalTauA(alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Goodman & Kruskal's Tau A similarity.

For two sets X and Y and a population N, Goodman & Kruskal's \(\tau_a\) similarity [GK54], by analogy with \(\tau_b\), is

\[sim_{GK_{\tau_a}}(X, Y) = \frac{\frac{\frac{|X \cap Y|}{|N|}^2 + \frac{|Y \setminus X|}{|N|}^2}{\frac{|Y|}{|N|}}+ \frac{\frac{|X \setminus Y|}{|N|}^2 + \frac{|(N \setminus X) \setminus Y|}{|N|}^2} {\frac{|N \setminus X|}{|N|}} - (\frac{|X|}{|N|}^2 + \frac{|N \setminus X|}{|N|}^2)} {1 - (\frac{|X|}{|N|}^2 + \frac{|N \setminus X|}{|N|}^2)}\]

In 2x2 confusion table terms, where a+b+c+d=n, after each term has been converted to a proportion by dividing by n, this is

\[sim_{GK_{\tau_a}} = \frac{ \frac{a^2 + c^2}{a+c} + \frac{b^2 + d^2}{b+d} - ((a+b)^2 + (c+d)^2)} {1 - ((a+b)^2 + (c+d)^2)}\]

New in version 0.4.0.

Initialize GoodmanKruskalTauA instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • normalizer (str) -- Specifies the normalization type. See normalizer description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Goodman & Kruskal's Tau A similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Goodman & Kruskal's Tau A similarity

Return type

float

Examples

>>> cmp = GoodmanKruskalTauA()
>>> cmp.sim('cat', 'hat')
0.3304969657208484
>>> cmp.sim('Niall', 'Neil')
0.22137604585914503
>>> cmp.sim('aluminum', 'Catalan')
0.05991264724130685
>>> cmp.sim('ATCG', 'TAGC')
4.119695274745721e-05

New in version 0.4.0.

class abydos.distance.GoodmanKruskalTauB(alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Goodman & Kruskal's Tau B similarity.

For two sets X and Y and a population N, Goodman & Kruskal's \(\tau_b\) similarity [GK54] is

\[sim_{GK_{\tau_b}}(X, Y) = \frac{\frac{\frac{|X \cap Y|}{|N|}^2 + \frac{|X \setminus Y|}{|N|}^2}{\frac{|X|}{|N|}}+ \frac{\frac{|Y \setminus X|}{|N|}^2 + \frac{|(N \setminus X) \setminus Y|}{|N|}^2} {\frac{|N \setminus X|}{|N|}} - (\frac{|Y|}{|N|}^2 + \frac{|N \setminus Y|}{|N|}^2)} {1 - (\frac{|Y|}{|N|}^2 + \frac{|N \setminus Y|}{|N|}^2)}\]

In 2x2 confusion table terms, where a+b+c+d=n, after each term has been converted to a proportion by dividing by n, this is

\[sim_{GK_{\tau_b}} = \frac{ \frac{a^2 + b^2}{a+b} + \frac{c^2 + d^2}{c+d} - ((a+c)^2 + (b+d)^2)} {1 - ((a+c)^2 + (b+d)^2)}\]

New in version 0.4.0.

Initialize GoodmanKruskalTauB instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • normalizer (str) -- Specifies the normalization type. See normalizer description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Goodman & Kruskal's Tau B similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Goodman & Kruskal's Tau B similarity

Return type

float

Examples

>>> cmp = GoodmanKruskalTauB()
>>> cmp.sim('cat', 'hat')
0.3304969657208484
>>> cmp.sim('Niall', 'Neil')
0.2346006486710202
>>> cmp.sim('aluminum', 'Catalan')
0.06533810992392582
>>> cmp.sim('ATCG', 'TAGC')
4.119695274745721e-05

New in version 0.4.0.

class abydos.distance.GowerLegendre(alphabet=None, tokenizer=None, intersection_type='crisp', theta=0.5, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Gower & Legendre similarity.

For two sets X and Y and a population N, the Gower & Legendre similarity [GL86] is

\[sim_{GowerLegendre}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|} {|X \cap Y| + |(N \setminus X) \setminus Y| + \theta \cdot |X \triangle Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{GowerLegendre} = \frac{a+d}{a+\theta(b+c)+d}\]

New in version 0.4.0.

Initialize GowerLegendre instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • theta (float) -- The weight to place on the symmetric difference.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Gower & Legendre similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gower & Legendre similarity

Return type

float

Examples

>>> cmp = GowerLegendre()
>>> cmp.sim('cat', 'hat')
0.9974424552429667
>>> cmp.sim('Niall', 'Neil')
0.9955156950672646
>>> cmp.sim('aluminum', 'Catalan')
0.9903536977491961
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516

New in version 0.4.0.

class abydos.distance.GuttmanLambdaA(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Guttman's Lambda A similarity.

For two sets X and Y and a population N, Guttman's \(\lambda_a\) similarity [Gut41] is

\[sim_{Guttman_{\lambda_a}}(X, Y) = \frac{max(|X \cap Y|, |Y \setminus X|) + max(|X \setminus Y|, |(N \setminus X) \setminus Y|) - max(|X|, |N \setminus X|)} {|N| - max(|X|, |N \setminus X|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Guttman_{\lambda_a}} = \frac{max(a, c) + max(b, d) - max(a+b, c+d)}{n - max(a+b, c+d)}\]

New in version 0.4.0.

Initialize GuttmanLambdaA instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Guttman Lambda A similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Guttman's Lambda A similarity

Return type

float

Examples

>>> cmp = GuttmanLambdaA()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.GuttmanLambdaB(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Guttman's Lambda B similarity.

For two sets X and Y and a population N, Guttman's \(\lambda_b\) similarity [Gut41] is

\[sim_{Guttman_{\lambda_b}}(X, Y) = \frac{max(|X \cap Y|, |X \setminus Y|) + max(|Y \setminus X|, |(N \setminus X) \setminus Y|) - max(|Y|, |N \setminus Y|)} {|N| - max(|Y|, |N \setminus Y|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Guttman_{\lambda_b}} = \frac{max(a, b) + max(c, d) - max(a+c, b+d)}{n - max(a+c, b+d)}\]

New in version 0.4.0.

Initialize GuttmanLambdaB instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Guttman Lambda B similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Guttman's Lambda B similarity

Return type

float

Examples

>>> cmp = GuttmanLambdaB()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.GwetAC(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Gwet's AC correlation.

For two sets X and Y and a population N, Gwet's AC correlation [Gwe08] is

\[corr_{Gwet_{AC}}(X, Y) = AC = \frac{p_o - p_e^{AC}}{1 - p_e^{AC}}\]

where

\[ \begin{align}\begin{aligned}\begin{array}{lll} p_o &=&\frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}\\p_e^{AC}&=&\frac{1}{2}\Big(\frac{|X|+|Y|}{|N|}\cdot \frac{|X \setminus Y| + |Y \setminus X|}{|N|}\Big) \end{array}\end{aligned}\end{align} \]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[ \begin{align}\begin{aligned}\begin{array}{lll} p_o&=&\frac{a+d}{n}\\p_e^{AC}&=&\frac{1}{2}\Big(\frac{2a+b+c}{n}\cdot \frac{2d+b+c}{n}\Big) \end{array}\end{aligned}\end{align} \]

New in version 0.4.0.

Initialize GwetAC instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Gwet's AC correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gwet's AC correlation

Return type

float

Examples

>>> cmp = GwetAC()
>>> cmp.corr('cat', 'hat')
0.9948456319360438
>>> cmp.corr('Niall', 'Neil')
0.990945276504824
>>> cmp.corr('aluminum', 'Catalan')
0.9804734301840141
>>> cmp.corr('ATCG', 'TAGC')
0.9870811678360627

New in version 0.4.0.

sim(src, tar)[source]

Return the Gwet's AC similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Gwet's AC similarity

Return type

float

Examples

>>> cmp = GwetAC()
>>> cmp.sim('cat', 'hat')
0.9974228159680218
>>> cmp.sim('Niall', 'Neil')
0.995472638252412
>>> cmp.sim('aluminum', 'Catalan')
0.9902367150920071
>>> cmp.sim('ATCG', 'TAGC')
0.9935405839180314

New in version 0.4.0.

class abydos.distance.Hamann(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Hamann correlation.

For two sets X and Y and a population N, the Hamann correlation [Ham61] is

\[corr_{Hamann}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y| - |X \setminus Y| - |Y \setminus X|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Hamann} = \frac{a+d-b-c}{n}\]

New in version 0.4.0.

Initialize Hamann instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Hamann correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Hamann correlation

Return type

float

Examples

>>> cmp = Hamann()
>>> cmp.corr('cat', 'hat')
0.9897959183673469
>>> cmp.corr('Niall', 'Neil')
0.9821428571428571
>>> cmp.corr('aluminum', 'Catalan')
0.9617834394904459
>>> cmp.corr('ATCG', 'TAGC')
0.9744897959183674

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Hamann similarity of two strings.

Hamann similarity, which has a range [-1, 1] is normalized to [0, 1] by adding 1 and dividing by 2.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Hamann similarity

Return type

float

Examples

>>> cmp = Hamann()
>>> cmp.sim('cat', 'hat')
0.9948979591836735
>>> cmp.sim('Niall', 'Neil')
0.9910714285714286
>>> cmp.sim('aluminum', 'Catalan')
0.9808917197452229
>>> cmp.sim('ATCG', 'TAGC')
0.9872448979591837

New in version 0.4.0.

class abydos.distance.HarrisLahey(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Harris & Lahey similarity.

For two sets X and Y and a population N, Harris & Lahey similarity [HL78] is

\[sim_{HarrisLahey}(X, Y) = \frac{|X \cap Y|}{|X \cup Y|}\cdot \frac{|N \setminus Y| + |N \setminus X|}{2|N|}+ \frac{|(N \setminus X) \setminus Y|}{|N \setminus (X \cap Y)|}\cdot \frac{|X| + |Y|}{2|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{HarrisLahey} = \frac{a}{a+b+c}\cdot\frac{2d+b+c}{2n}+ \frac{d}{d+b+c}\cdot\frac{2a+b+c}{2n}\]

Notes

Most catalogs of similarity coefficients [War08][Mor12][Xia13] omit the \(n\) terms in the denominators, but the worked example in [HL78] makes it clear that this is intended in the original.

New in version 0.4.0.

Initialize HarrisLahey instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Harris & Lahey similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Harris & Lahey similarity

Return type

float

Examples

>>> cmp = HarrisLahey()
>>> cmp.sim('cat', 'hat')
0.3367085964820711
>>> cmp.sim('Niall', 'Neil')
0.22761577457069784
>>> cmp.sim('aluminum', 'Catalan')
0.07244410503054725
>>> cmp.sim('ATCG', 'TAGC')
0.006296204706372345

New in version 0.4.0.

class abydos.distance.Hassanat(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Hassanat distance.

For two multisets X and Y drawn from an alphabet S, Hassanat distance [Has14] is

\[dist_{Hassanat}(X, Y) = \sum_{i \in S} D(X_i, Y_i)\]

where

\[\begin{split}D(X_i, Y_i) = \left\{\begin{array}{ll} 1-\frac{1+min(X_i, Y_i)}{1+max(X_i, Y_i)}&, min(X_i, Y_i) \geq 0 \\ \\ 1-\frac{1+min(X_i, Y_i)+|min(X_i, Y_i)|} {1+max(X_i, Y_i)+|min(X_i, Y_i)|}&, min(X_i, Y_i) < 0 \end{array}\right.\end{split}\]

New in version 0.4.0.

Initialize Hassanat instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Hassanat distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Hassanat distance

Return type

float

Examples

>>> cmp = Hassanat()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.3888888888888889
>>> cmp.dist('aluminum', 'Catalan')
0.4777777777777778
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Hassanat distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Hassanat distance

Return type

float

Examples

>>> cmp = Hassanat()
>>> cmp.dist_abs('cat', 'hat')
2.0
>>> cmp.dist_abs('Niall', 'Neil')
3.5
>>> cmp.dist_abs('aluminum', 'Catalan')
7.166666666666667
>>> cmp.dist_abs('ATCG', 'TAGC')
5.0

New in version 0.4.0.

class abydos.distance.HawkinsDotson(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Hawkins & Dotson similarity.

For two sets X and Y and a population N, Hawkins & Dotson similarity [HD73] is the mean of the occurrence agreement and non-occurrence agreement

\[sim_{HawkinsDotson}(X, Y) = \frac{1}{2}\cdot\Big( \frac{|X \cap Y|}{|X \cup Y|}+ \frac{|(N \setminus X) \setminus Y|}{|N \setminus (X \cap Y)|} \Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{HawkinsDotson} = \frac{1}{2}\cdot\Big(\frac{a}{a+b+c}+\frac{d}{b+c+d}\Big)\]

New in version 0.4.0.

Initialize HawkinsDotson instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Hawkins & Dotson similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Hawkins & Dotson similarity

Return type

float

Examples

>>> cmp = HawkinsDotson()
>>> cmp.sim('cat', 'hat')
0.6641091219096334
>>> cmp.sim('Niall', 'Neil')
0.606635407786303
>>> cmp.sim('aluminum', 'Catalan')
0.5216836734693877
>>> cmp.sim('ATCG', 'TAGC')
0.49362244897959184

New in version 0.4.0.

class abydos.distance.Hellinger(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Hellinger distance.

For two multisets X and Y drawn from an alphabet S, Hellinger distance [Hel09] is

\[dist_{Hellinger}(X, Y) = \sqrt{2 \cdot \sum_{i \in S} (\sqrt{|A_i|} - \sqrt{|B_i|})^2}\]

New in version 0.4.0.

Initialize Hellinger instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Hellinger distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Hellinger distance

Return type

float

Examples

>>> cmp = Hellinger()
>>> cmp.dist('cat', 'hat')
0.8164965809277261
>>> cmp.dist('Niall', 'Neil')
0.881917103688197
>>> cmp.dist('aluminum', 'Catalan')
0.9128709291752769
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Hellinger distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Hellinger distance

Return type

float

Examples

>>> cmp = Hellinger()
>>> cmp.dist_abs('cat', 'hat')
2.8284271247461903
>>> cmp.dist_abs('Niall', 'Neil')
3.7416573867739413
>>> cmp.dist_abs('aluminum', 'Catalan')
5.477225575051661
>>> cmp.dist_abs('ATCG', 'TAGC')
4.47213595499958

New in version 0.4.0.

class abydos.distance.HendersonHeron(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Henderson-Heron dissimilarity.

For two sets X and Y and a population N, Henderson-Heron dissimilarity [HH77] is:

New in version 0.4.1.

Initialize HendersonHeron instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist(src, tar)[source]

Return the Henderson-Heron dissimilarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Henderson-Heron dissimilarity

Return type

float

Examples

>>> cmp = HendersonHeron()
>>> cmp.dist('cat', 'hat')
0.00011668873858680838
>>> cmp.dist('Niall', 'Neil')
0.00048123075776606097
>>> cmp.dist('aluminum', 'Catalan')
0.08534181060514882
>>> cmp.dist('ATCG', 'TAGC')
0.9684367974410505

New in version 0.4.1.

class abydos.distance.HornMorisita(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Horn-Morisita index of overlap.

Horn-Morisita index of overlap [Hor66], given two populations X and Y drawn from S species, is:

\[sim_{Horn-Morisita}(X, Y) = C_{\lambda} = \frac{2\sum_{i=1}^S x_i y_i} {(\hat{\lambda}_x + \hat{\lambda}_y)XY}\]

where

\[X = \sum_{i=1}^S x_i ~~;~~ Y = \sum_{i=1}^S y_i\]
\[\hat{\lambda}_x = \frac{\sum_{i=1}^S x_i^2}{X^2} ~~;~~ \hat{\lambda}_y = \frac{\sum_{i=1}^S y_i^2}{Y^2}\]

Observe that this is identical to Morisita similarity, except for the definition of the \(\lambda\) values in the denominator.

New in version 0.4.1.

Initialize HornMorisita instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

sim(src, tar)[source]

Return the Horn-Morisita similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Horn-Morisita similarity

Return type

float

Examples

>>> cmp = HornMorisita()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3636363636363636
>>> cmp.sim('aluminum', 'Catalan')
0.10650887573964497
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.1.

class abydos.distance.Hurlbert(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Hurlbert correlation.

In 2x2 confusion table terms, where a+b+c+d=n, Hurlbert's coefficient of interspecific association [Hur69] is

\[corr_{Hurlbert} = \frac{ad-bc}{|ad-bc|} \sqrt{\frac{Obs_{\chi^2}-Min_{\chi^2}} {Max_{\chi^2}-Min_{\chi^2}}}\]

Where:

\[ \begin{align}\begin{aligned}\begin{array}{lll} Obs_{\chi^2} &= \frac{(ad-bc)^2n}{(a+b)(a+c)(b+d)(c+d)}\\Max_{\chi^2} &= \frac{(a+b)(b+d)n}{(a+c)(c+d)} &\textrm{ when } ad \geq bc\\Max_{\chi^2} &= \frac{(a+b)(a+c)n}{(b+d)(c+d)} &\textrm{ when } ad < bc \textrm{ and } a \leq d\\Max_{\chi^2} &= \frac{(b+d)(c+d)n}{(a+b)(a+c)} &\textrm{ when } ad < bc \textrm{ and } a > d\\Min_{\chi^2} &= \frac{n^3 (\hat{a} - g(\hat{a}))^2} {(a+b)(a+c)(c+d)(b+d)}\\\textrm{where } \hat{a} &= \frac{(a+b)(a+c)}{n}\\\textrm{and } g(\hat{a}) &= \lfloor\hat{a}\rfloor &\textrm{ when } ad < bc,\\\textrm{otherwise } g(\hat{a}) &= \lceil\hat{a}\rceil \end{array}\end{aligned}\end{align} \]

New in version 0.4.0.

Initialize Hurlbert instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Hurlbert correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Hurlbert correlation

Return type

float

Examples

>>> cmp = Hurlbert()
>>> cmp.corr('cat', 'hat')
0.497416003373807
>>> cmp.corr('Niall', 'Neil')
0.32899851514665707
>>> cmp.corr('aluminum', 'Catalan')
0.10144329225459262
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Hurlbert similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Hurlbert similarity

Return type

float

Examples

>>> cmp = Hurlbert()
>>> cmp.sim('cat', 'hat')
0.7487080016869034
>>> cmp.sim('Niall', 'Neil')
0.6644992575733285
>>> cmp.sim('aluminum', 'Catalan')
0.5507216461272963
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Jaccard(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._tversky.Tversky

Jaccard similarity.

For two sets X and Y, the Jaccard similarity coefficient [Jac01][Rruvzivcka58] is

\[sim_{Jaccard}(X, Y) = \frac{|X \cap Y|}{|X \cup Y|}`.\]

This is identical to the Tanimoto similarity coefficient [Tan58] and the Tversky index [Tve77] for \(\alpha = \beta = 1\).

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Jaccard} = \frac{a}{a+b+c}\]

Notes

The multiset variant is termed Ellenberg similarity [Ell56].

New in version 0.3.6.

Initialize Jaccard instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Jaccard similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Jaccard similarity

Return type

float

Examples

>>> cmp = Jaccard()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.2222222222222222
>>> cmp.sim('aluminum', 'Catalan')
0.0625
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

tanimoto_coeff(src, tar)[source]

Return the Tanimoto distance between two strings.

Tanimoto distance [Tan58] is \(-log_{2} sim_{Tanimoto}(X, Y)\).

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tanimoto distance

Return type

float

Examples

>>> cmp = Jaccard()
>>> cmp.tanimoto_coeff('cat', 'hat')
-1.5849625007211563
>>> cmp.tanimoto_coeff('Niall', 'Neil')
-2.1699250014423126
>>> cmp.tanimoto_coeff('aluminum', 'Catalan')
-4.0
>>> cmp.tanimoto_coeff('ATCG', 'TAGC')
-inf

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_jaccard(src, tar, qval=2)[source]

Return the Jaccard distance between two strings.

This is a wrapper for Jaccard.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Jaccard distance

Return type

float

Examples

>>> dist_jaccard('cat', 'hat')
0.6666666666666667
>>> dist_jaccard('Niall', 'Neil')
0.7777777777777778
>>> dist_jaccard('aluminum', 'Catalan')
0.9375
>>> dist_jaccard('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Jaccard.dist method instead.

abydos.distance.sim_jaccard(src, tar, qval=2)[source]

Return the Jaccard similarity of two strings.

This is a wrapper for Jaccard.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Jaccard similarity

Return type

float

Examples

>>> sim_jaccard('cat', 'hat')
0.3333333333333333
>>> sim_jaccard('Niall', 'Neil')
0.2222222222222222
>>> sim_jaccard('aluminum', 'Catalan')
0.0625
>>> sim_jaccard('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Jaccard.sim method instead.

abydos.distance.tanimoto(src, tar, qval=2)[source]

Return the Tanimoto coefficient of two strings.

This is a wrapper for Jaccard.tanimoto_coeff().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Tanimoto distance

Return type

float

Examples

>>> tanimoto('cat', 'hat')
-1.5849625007211563
>>> tanimoto('Niall', 'Neil')
-2.1699250014423126
>>> tanimoto('aluminum', 'Catalan')
-4.0
>>> tanimoto('ATCG', 'TAGC')
-inf

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Jaccard.tanimoto_coeff method instead.

class abydos.distance.JaccardNM(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Jaccard-NM similarity.

For two sets X and Y and a population N, Jaccard-NM similarity [NMM11] is

\[sim_{JaccardNM}(X, Y) = \frac{|X \cap Y|} {|N| + |X \cap Y| + |X \setminus Y| + |Y \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{JaccardNM} = \frac{a}{2(a+b+c)+d}\]

New in version 0.4.0.

Initialize JaccardNM instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Jaccard-NM similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Jaccard-NM similarity

Return type

float

Examples

>>> cmp = JaccardNM()
>>> cmp.sim('cat', 'hat')
0.005063291139240506
>>> cmp.sim('Niall', 'Neil')
0.005044136191677175
>>> cmp.sim('aluminum', 'Catalan')
0.0024968789013732834
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Jaccard-NM similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Jaccard-NM similarity

Return type

float

Examples

>>> cmp = JaccardNM()
>>> cmp.sim_score('cat', 'hat')
0.002531645569620253
>>> cmp.sim_score('Niall', 'Neil')
0.0025220680958385876
>>> cmp.sim_score('aluminum', 'Catalan')
0.0012484394506866417
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Johnson(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Johnson similarity.

For two sets X and Y, the Johnson similarity [Joh67] is

\[sim_{Johnson}(X, Y) = \frac{(|X \cap Y|}{|X|} + \frac{|Y \cap X}{|Y|}`.\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Johnson} = \frac{a}{a+b}+\frac{a}{a+c}\]

New in version 0.4.0.

Initialize Johnson instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Johnson similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Johnson similarity

Return type

float

Examples

>>> cmp = Johnson()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3666666666666667
>>> cmp.sim('aluminum', 'Catalan')
0.11805555555555555
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Johnson similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Johnson similarity

Return type

float

Examples

>>> cmp = Johnson()
>>> cmp.sim_score('cat', 'hat')
1.0
>>> cmp.sim_score('Niall', 'Neil')
0.7333333333333334
>>> cmp.sim_score('aluminum', 'Catalan')
0.2361111111111111
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.KendallTau(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kendall's Tau correlation.

For two sets X and Y and a population N, Kendall's Tau correlation [Ken38] is

\[corr_{KendallTau}(X, Y) = \frac{2 \cdot (|X \cap Y| + |(N \setminus X) \setminus Y| - |X \triangle Y|)}{|N| \cdot (|N|-1)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KendallTau} = \frac{2 \cdot (a+d-b-c)}{n \cdot (n-1)}\]

New in version 0.4.0.

Initialize KendallTau instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kendall's Tau correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kendall's Tau correlation

Return type

float

Examples

>>> cmp = KendallTau()
>>> cmp.corr('cat', 'hat')
0.0025282143508744493
>>> cmp.corr('Niall', 'Neil')
0.00250866630176975
>>> cmp.corr('aluminum', 'Catalan')
0.0024535291823735866
>>> cmp.corr('ATCG', 'TAGC')
0.0024891182526650506

Notes

This correlation is not necessarily bounded to [-1.0, 1.0], but will typically be within these bounds for real data.

New in version 0.4.0.

sim(src, tar)[source]

Return the Kendall's Tau similarity of two strings.

The Tau correlation is first clamped to the range [-1.0, 1.0] before being converted to a similarity value to ensure that the similarity is in the range [0.0, 1.0].

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kendall's Tau similarity

Return type

float

Examples

>>> cmp = KendallTau()
>>> cmp.sim('cat', 'hat')
0.5012641071754372
>>> cmp.sim('Niall', 'Neil')
0.5012543331508849
>>> cmp.sim('aluminum', 'Catalan')
0.5012267645911868
>>> cmp.sim('ATCG', 'TAGC')
0.5012445591263325

New in version 0.4.0.

class abydos.distance.KentFosterI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kent & Foster I similarity.

For two sets X and Y and a population N, Kent & Foster I similarity [KF77], \(K_{occ}\), is

\[sim_{KentFosterI}(X, Y) = \frac{|X \cap Y| - \frac{|X|\cdot|Y|}{|X \cup Y|}} {|X \cap Y| - \frac{|X|\cdot|Y|}{|X \cup Y|} + |X \setminus Y| + |Y \setminus X|}\]

Kent & Foster derived this from Cohen's \(\kappa\) by "subtracting appropriate chance agreement correction figures from the numerators and denominators" to arrive at an occurrence reliability measure.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KentFosterI} = \frac{a-\frac{(a+b)(a+c)}{a+b+c}}{a-\frac{(a+b)(a+c)}{a+b+c}+b+c}\]

New in version 0.4.0.

Initialize KentFosterI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Kent & Foster I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Kent & Foster I similarity

Return type

float

Examples

>>> cmp = KentFosterI()
>>> cmp.sim('cat', 'hat')
0.8
>>> cmp.sim('Niall', 'Neil')
0.7647058823529411
>>> cmp.sim('aluminum', 'Catalan')
0.6956521739130435
>>> cmp.sim('ATCG', 'TAGC')
0.6666666666666667

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Kent & Foster I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kent & Foster I similarity

Return type

float

Examples

>>> cmp = KentFosterI()
>>> cmp.sim_score('cat', 'hat')
-0.19999999999999996
>>> cmp.sim_score('Niall', 'Neil')
-0.23529411764705888
>>> cmp.sim_score('aluminum', 'Catalan')
-0.30434782608695654
>>> cmp.sim_score('ATCG', 'TAGC')
-0.3333333333333333

New in version 0.4.0.

class abydos.distance.KentFosterII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kent & Foster II similarity.

For two sets X and Y and a population N, Kent & Foster II similarity [KF77], \(K_{nonocc}\), is

\[sim_{KentFosterII}(X, Y) = \frac{|(N \setminus X) \setminus Y| - \frac{|X \setminus Y|\cdot|Y \setminus X|} {|N \setminus (X \cap Y)|}} {|(N \setminus X) \setminus Y| - \frac{|X \setminus Y|\cdot|Y \setminus X|} {|N \setminus (X \cap Y)|} + |X \setminus Y| + |Y \setminus X|}\]

Kent & Foster derived this from Cohen's \(\kappa\) by "subtracting appropriate chance agreement correction figures from the numerators and denominators" to arrive at an non-occurrence reliability measure.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KentFosterII} = \frac{d-\frac{(b+d)(c+d)}{b+c+d}}{d-\frac{(b+d)(c+d)}{b+c+d}+b+c}\]

New in version 0.4.0.

Initialize KentFosterII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Kent & Foster II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Kent & Foster II similarity

Return type

float

Examples

>>> cmp = KentFosterII()
>>> cmp.sim('cat', 'hat')
0.998719590268876
>>> cmp.sim('Niall', 'Neil')
0.9978030025631628
>>> cmp.sim('aluminum', 'Catalan')
0.9952153110047858
>>> cmp.sim('ATCG', 'TAGC')
0.9968010236724241

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Kent & Foster II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kent & Foster II similarity

Return type

float

Examples

>>> cmp = KentFosterII()
>>> cmp.sim_score('cat', 'hat')
-0.0012804097311239404
>>> cmp.sim_score('Niall', 'Neil')
-0.002196997436837158
>>> cmp.sim_score('aluminum', 'Catalan')
-0.004784688995214218
>>> cmp.sim_score('ATCG', 'TAGC')
-0.0031989763275758767

New in version 0.4.0.

class abydos.distance.KoppenI(alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Köppen I correlation.

For two sets X and Y and an alphabet N, provided that \(|X| = |Y|\), Köppen I correlation [Koppen70][GK59] is

\[corr_{KoppenI}(X, Y) = \frac{|X| \cdot |N \setminus X| - |X \setminus Y|} {|X| \cdot |N \setminus X|}\]

To support cases where \(|X| \neq |Y|\), this class implements a slight variation, while still providing the expected results when \(|X| = |Y|\):

\[corr_{KoppenI}(X, Y) = \frac{\frac{|X|+|Y|}{2} \cdot \frac{|N \setminus X|+|N \setminus Y|}{2}- \frac{|X \triangle Y|}{2}} {\frac{|X|+|Y|}{2} \cdot \frac{|N \setminus X|+|N \setminus Y|}{2}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KoppenI} = \frac{\frac{2a+b+c}{2} \cdot \frac{2d+b+c}{2}- \frac{b+c}{2}} {\frac{2a+b+c}{2} \cdot \frac{2d+b+c}{2}}\]

Notes

In the usual case all of the above values should be proportional to the total number of samples n. I.e., a, b, c, d, & n should all be divided by n prior to calculating the coefficient. This class's default normalizer is, accordingly, 'proportional'.

New in version 0.4.0.

Initialize KoppenI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • normalizer (str) -- Specifies the normalization type. See normalizer description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Köppen I correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Köppen I correlation

Return type

float

Examples

>>> cmp = KoppenI()
>>> cmp.corr('cat', 'hat')
0.49615384615384617
>>> cmp.corr('Niall', 'Neil')
0.3575056927658083
>>> cmp.corr('aluminum', 'Catalan')
0.1068520131813188
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483896

New in version 0.4.0.

sim(src, tar)[source]

Return the Köppen I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Köppen I similarity

Return type

float

Examples

>>> cmp = KoppenI()
>>> cmp.sim('cat', 'hat')
0.7480769230769231
>>> cmp.sim('Niall', 'Neil')
0.6787528463829041
>>> cmp.sim('aluminum', 'Catalan')
0.5534260065906594
>>> cmp.sim('ATCG', 'TAGC')
0.49679075738125805

New in version 0.4.0.

class abydos.distance.KoppenII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Köppen II similarity.

For two sets X and Y, Köppen II similarity [Koppen70][GK59] is

\[sim_{KoppenII}(X, Y) = |X \cap Y| + \frac{|X \setminus Y| + |Y \setminus X|}{2}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KoppenII} = a + \frac{b+c}{2}\]

New in version 0.4.0.

Initialize KoppenII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Köppen II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Köppen II similarity

Return type

float

Examples

>>> cmp = KoppenII()
>>> cmp.sim('cat', 'hat')
0.6666666666666666
>>> cmp.sim('Niall', 'Neil')
0.6111111111111112
>>> cmp.sim('aluminum', 'Catalan')
0.53125
>>> cmp.sim('ATCG', 'TAGC')
0.5

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Köppen II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Köppen II similarity

Return type

float

Examples

>>> cmp = KoppenII()
>>> cmp.sim_score('cat', 'hat')
4.0
>>> cmp.sim_score('Niall', 'Neil')
5.5
>>> cmp.sim_score('aluminum', 'Catalan')
8.5
>>> cmp.sim_score('ATCG', 'TAGC')
5.0

New in version 0.4.0.

class abydos.distance.KuderRichardson(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuder & Richardson correlation.

For two sets X and Y and a population N, Kuder & Richardson similarity [KR37][Cro51] is

\[corr_{KuderRichardson}(X, Y) = \frac{4(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)} {|X| \cdot |N \setminus X| + |Y| \cdot |N \setminus Y| + 2(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuderRichardson} = \frac{4(ad-bc)}{(a+b)(c+d) + (a+c)(b+d) +2(ad-bc)}\]

New in version 0.4.0.

Initialize KuderRichardson instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuder & Richardson correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuder & Richardson correlation

Return type

float

Examples

>>> cmp = KuderRichardson()
>>> cmp.corr('cat', 'hat')
0.6643835616438356
>>> cmp.corr('Niall', 'Neil')
0.5285677463699631
>>> cmp.corr('aluminum', 'Catalan')
0.19499521400246136
>>> cmp.corr('ATCG', 'TAGC')
-0.012919896640826873

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuder & Richardson similarity of two strings.

Since Kuder & Richardson correlation is unbounded in the negative, this measure is first clamped to [-1.0, 1.0].

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuder & Richardson similarity

Return type

float

Examples

>>> cmp = KuderRichardson()
>>> cmp.sim('cat', 'hat')
0.8321917808219178
>>> cmp.sim('Niall', 'Neil')
0.7642838731849815
>>> cmp.sim('aluminum', 'Catalan')
0.5974976070012307
>>> cmp.sim('ATCG', 'TAGC')
0.4935400516795866

New in version 0.4.0.

class abydos.distance.KuhnsI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns I correlation.

For two sets X and Y and a population N, Kuhns I correlation [Kuh64], the excess of separation over its independence value (S), is

\[corr_{KuhnsI}(X, Y) = \frac{2\delta(X, Y)}{|N|}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsI} = \frac{2\delta(a+b, a+c)}{n}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns I correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns I correlation

Return type

float

Examples

>>> cmp = KuhnsI()
>>> cmp.corr('cat', 'hat')
0.005049979175343606
>>> cmp.corr('Niall', 'Neil')
0.005004425239483548
>>> cmp.corr('aluminum', 'Catalan')
0.0023140898210880765
>>> cmp.corr('ATCG', 'TAGC')
-8.134631403581842e-05

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns I similarity

Return type

float

Examples

>>> cmp = KuhnsI()
>>> cmp.sim('cat', 'hat')
0.5050499791753436
>>> cmp.sim('Niall', 'Neil')
0.5050044252394835
>>> cmp.sim('aluminum', 'Catalan')
0.502314089821088
>>> cmp.sim('ATCG', 'TAGC')
0.49991865368596416

New in version 0.4.0.

class abydos.distance.KuhnsII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns II correlation.

For two sets X and Y and a population N, Kuhns II correlation [Kuh64], the excess of rectangular distance over its independence value (R), is

\[corr_{KuhnsII}(X, Y) = \frac{\delta(X, Y)}{max(|X|, |Y|)}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsII} = \frac{\delta(a+b, a+c)}{max(a+b, a+c)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns II correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns II correlation

Return type

float

Examples

>>> cmp = KuhnsII()
>>> cmp.corr('cat', 'hat')
0.49489795918367346
>>> cmp.corr('Niall', 'Neil')
0.32695578231292516
>>> cmp.corr('aluminum', 'Catalan')
0.10092002830856334
>>> cmp.corr('ATCG', 'TAGC')
-0.006377551020408163

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns II similarity

Return type

float

Examples

>>> cmp = KuhnsII()
>>> cmp.sim('cat', 'hat')
0.663265306122449
>>> cmp.sim('Niall', 'Neil')
0.5513038548752834
>>> cmp.sim('aluminum', 'Catalan')
0.40061335220570893
>>> cmp.sim('ATCG', 'TAGC')
0.32908163265306123

New in version 0.4.0.

class abydos.distance.KuhnsIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns III correlation.

For two sets X and Y and a population N, Kuhns III correlation [Kuh64], the excess of proportion of overlap over its independence value (P), is

\[corr_{KuhnsIII}(X, Y) = \frac{\delta(X, Y)}{\big(1-\frac{|X \cap Y|}{|X|+|Y|}\big) \big(|X|+|Y|-\frac{|X|\cdot|Y|}{|N|}\big)}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsIII} = \frac{\delta(a+b, a+c)}{\big(1-\frac{a}{2a+b+c}\big) \big(2a+b+c-\frac{(a+b)(a+c)}{n}\big)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

Notes

The coefficient presented in [Eid14][Mor12] as Kuhns' "Proportion of overlap above independence" is a significantly different coefficient, not evidenced in [Kuh64].

New in version 0.4.0.

Initialize KuhnsIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns III correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns III correlation

Return type

float

Examples

>>> cmp = KuhnsIII()
>>> cmp.corr('cat', 'hat')
0.3307757885763001
>>> cmp.corr('Niall', 'Neil')
0.21873141468207793
>>> cmp.corr('aluminum', 'Catalan')
0.05707545392902886
>>> cmp.corr('ATCG', 'TAGC')
-0.003198976327575176

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns III similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns III similarity

Return type

float

Examples

>>> cmp = KuhnsIII()
>>> cmp.sim('cat', 'hat')
0.498081841432225
>>> cmp.sim('Niall', 'Neil')
0.41404856101155846
>>> cmp.sim('aluminum', 'Catalan')
0.29280659044677165
>>> cmp.sim('ATCG', 'TAGC')
0.24760076775431863

New in version 0.4.0.

class abydos.distance.KuhnsIV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns IV correlation.

For two sets X and Y and a population N, Kuhns IV correlation [Kuh64], the excess of conditional probabilities over its independence value (W), is

\[corr_{KuhnsIV}(X, Y) = \frac{\delta(X, Y)}{min(|X|, |Y|)}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsIV} = \frac{\delta(a+b, a+c)}{min(a+b, a+c)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsIV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns IV correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns IV correlation

Return type

float

Examples

>>> cmp = KuhnsIV()
>>> cmp.corr('cat', 'hat')
0.49489795918367346
>>> cmp.corr('Niall', 'Neil')
0.3923469387755102
>>> cmp.corr('aluminum', 'Catalan')
0.11353503184713376
>>> cmp.corr('ATCG', 'TAGC')
-0.006377551020408163

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns IV similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns IV similarity

Return type

float

Examples

>>> cmp = KuhnsIV()
>>> cmp.sim('cat', 'hat')
0.7474489795918368
>>> cmp.sim('Niall', 'Neil')
0.696173469387755
>>> cmp.sim('aluminum', 'Catalan')
0.5567675159235669
>>> cmp.sim('ATCG', 'TAGC')
0.4968112244897959

New in version 0.4.0.

class abydos.distance.KuhnsV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns V correlation.

For two sets X and Y and a population N, Kuhns V correlation [Kuh64], the excess of probability differences U over its independence value (U), is

\[corr_{KuhnsV}(X, Y) = \frac{\delta(X, Y)} {max\big(|X|\cdot(1-\frac{|X|}{|N|}), |Y|\cdot(1-\frac{|Y|}{|N|})\big)}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsV} = \frac{\delta(a+b, a+c)} {max\big((a+b)(1-\frac{a+b}{n}), (a+c)(1-\frac{a+c}{n})\big)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns V correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns V correlation

Return type

float

Examples

>>> cmp = KuhnsV()
>>> cmp.corr('cat', 'hat')
0.497435897435897
>>> cmp.corr('Niall', 'Neil')
0.329477292202228
>>> cmp.corr('aluminum', 'Catalan')
0.10209049255441
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237484

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns V similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns V similarity

Return type

float

Examples

>>> cmp = KuhnsV()
>>> cmp.sim('cat', 'hat')
0.7487179487179485
>>> cmp.sim('Niall', 'Neil')
0.664738646101114
>>> cmp.sim('aluminum', 'Catalan')
0.551045246277205
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.KuhnsVI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns VI correlation.

For two sets X and Y and a population N, Kuhns VI correlation [Kuh64], the excess of probability differences V over its independence value (V), is

\[corr_{KuhnsVI}(X, Y) = \frac{\delta(X, Y)} {min\big(|X|\cdot(1-\frac{|X|}{|N|}), |Y|(1-\frac{|Y|}{|N|})\big)}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsVI} = \frac{\delta(a+b, a+c)} {min\big((a+b)(1-\frac{a+b}{n}), (a+c)(1-\frac{a+c}{n})\big)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsVI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns VI correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns VI correlation

Return type

float

Examples

>>> cmp = KuhnsVI()
>>> cmp.corr('cat', 'hat')
0.497435897435897
>>> cmp.corr('Niall', 'Neil')
0.394865211810013
>>> cmp.corr('aluminum', 'Catalan')
0.11470398970399
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237484

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns VI similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns VI similarity

Return type

float

Examples

>>> cmp = KuhnsVI()
>>> cmp.sim('cat', 'hat')
0.7487179487179485
>>> cmp.sim('Niall', 'Neil')
0.6974326059050064
>>> cmp.sim('aluminum', 'Catalan')
0.557351994851995
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.KuhnsVII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns VII correlation.

For two sets X and Y and a population N, Kuhns VII correlation [Kuh64], the excess of angle between vector over its independence value (G), is

\[corr_{KuhnsVII}(X, Y) = \frac{\delta(X, Y)}{\sqrt{|X|\cdot|Y|}}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsVII} = \frac{\delta(a+b, a+c)}{\sqrt{(a+b)(a+c)}}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsVII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns VII correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns VII correlation

Return type

float

Examples

>>> cmp = KuhnsVII()
>>> cmp.corr('cat', 'hat')
0.49489795918367346
>>> cmp.corr('Niall', 'Neil')
0.3581621145590755
>>> cmp.corr('aluminum', 'Catalan')
0.10704185456178524
>>> cmp.corr('ATCG', 'TAGC')
-0.006377551020408163

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns VII similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns VII similarity

Return type

float

Examples

>>> cmp = KuhnsVII()
>>> cmp.sim('cat', 'hat')
0.663265306122449
>>> cmp.sim('Niall', 'Neil')
0.572108076372717
>>> cmp.sim('aluminum', 'Catalan')
0.40469456970785683
>>> cmp.sim('ATCG', 'TAGC')
0.32908163265306123

New in version 0.4.0.

class abydos.distance.KuhnsVIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns VIII correlation.

For two sets X and Y and a population N, Kuhns VIII correlation [Kuh64], the excess of coefficient by the arithmetic mean over its independence value (E), is

\[corr_{KuhnsVIII}(X, Y) = \frac{\delta(X, Y)}{|X \cap Y|+\frac{1}{2}\cdot|X \triangle Y|}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsVIII} = \frac{\delta(a+b, a+c)}{a+\frac{1}{2}(b+c)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

Notes

The coefficient presented in [Eid14][Mor12] as Kuhns' "Coefficient of arithmetic means" is a significantly different coefficient, not evidenced in [Kuh64].

New in version 0.4.0.

Initialize KuhnsVIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns VIII correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns VIII correlation

Return type

float

Examples

>>> cmp = KuhnsVIII()
>>> cmp.corr('cat', 'hat')
0.49489795918367346
>>> cmp.corr('Niall', 'Neil')
0.35667903525046385
>>> cmp.corr('aluminum', 'Catalan')
0.10685650056200824
>>> cmp.corr('ATCG', 'TAGC')
-0.006377551020408163

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns VIII similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns VIII similarity

Return type

float

Examples

>>> cmp = KuhnsVIII()
>>> cmp.sim('cat', 'hat')
0.663265306122449
>>> cmp.sim('Niall', 'Neil')
0.5711193568336426
>>> cmp.sim('aluminum', 'Catalan')
0.40457100037467214
>>> cmp.sim('ATCG', 'TAGC')
0.32908163265306123

New in version 0.4.0.

class abydos.distance.KuhnsIX(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns IX correlation.

For two sets X and Y and a population N, Kuhns IX correlation [Kuh64], the excess of coefficient of linear correlation over its independence value (L), is

\[corr_{KuhnsIX}(X, Y) = \frac{\delta(X, Y)}{\sqrt{|X|\cdot|Y|\cdot(1-\frac{|X|}{|N|}) \cdot(1-\frac{|Y|}{|N|})}}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsIX} = \frac{\delta(a+b, a+c)}{\sqrt{(a+b)(a+c)(1-\frac{a+b}{n}) (1-\frac{a+c}{n})}}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsIX instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns IX correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns IX correlation

Return type

float

Examples

>>> cmp = KuhnsIX()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.36069255713421955
>>> cmp.corr('aluminum', 'Catalan')
0.10821361655002706
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns IX similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns IX similarity

Return type

float

Examples

>>> cmp = KuhnsIX()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6803462785671097
>>> cmp.sim('aluminum', 'Catalan')
0.5541068082750136
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.KuhnsX(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns X correlation.

For two sets X and Y and a population N, Kuhns X correlation [Kuh64], the excess of Yule's Q over its independence value (Q), is

\[corr_{KuhnsX}(X, Y) = \frac{|N| \cdot \delta(X, Y)}{|X \cap Y| \cdot |(N \setminus X) \setminus Y| + |X \setminus Y| \cdot |Y \setminus X|}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsX} = \frac{n \cdot \delta(a+b, a+c)}{ad+bc}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsX instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns X correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns X correlation

Return type

float

Examples

>>> cmp = KuhnsX()
>>> cmp.corr('cat', 'hat')
0.994871794871795
>>> cmp.corr('Niall', 'Neil')
0.984635083226633
>>> cmp.corr('aluminum', 'Catalan')
0.864242424242424
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns X similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns X similarity

Return type

float

Examples

>>> cmp = KuhnsX()
>>> cmp.sim('cat', 'hat')
0.9974358974358974
>>> cmp.sim('Niall', 'Neil')
0.9923175416133165
>>> cmp.sim('aluminum', 'Catalan')
0.932121212121212
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.KuhnsXI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns XI correlation.

For two sets X and Y and a population N, Kuhns XI correlation [Kuh64], the excess of Yule's Y over its independence value (Y), is

\[corr_{KuhnsXI}(X, Y) = \frac{|N| \cdot \delta(X, Y)}{(\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + \sqrt{|X \setminus Y| \cdot |Y \setminus X|})^2}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{KuhnsXI} = \frac{n \cdot \delta(a+b, a+c)}{(\sqrt{ad}+\sqrt{bc})^2}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsXI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Kuhns XI correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns XI correlation

Return type

float

Examples

>>> cmp = KuhnsXI()
>>> cmp.corr('cat', 'hat')
0.9034892632818761
>>> cmp.corr('Niall', 'Neil')
0.8382551144735259
>>> cmp.corr('aluminum', 'Catalan')
0.5749826820237787
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Kuhns XI similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns XI similarity

Return type

float

Examples

>>> cmp = KuhnsXI()
>>> cmp.sim('cat', 'hat')
0.951744631640938
>>> cmp.sim('Niall', 'Neil')
0.919127557236763
>>> cmp.sim('aluminum', 'Catalan')
0.7874913410118893
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.KuhnsXII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kuhns XII similarity.

For two sets X and Y and a population N, Kuhns XII similarity [Kuh64], the excess of index of independence over its independence value (I), is

\[sim_{KuhnsXII}(X, Y) = \frac{|N| \cdot \delta(X, Y)}{|X| \cdot |Y|}\]

where

\[\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KuhnsXII} = \frac{n \cdot \delta(a+b, a+c)}{(a+b)(a+c)}\]

where

\[\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}\]

New in version 0.4.0.

Initialize KuhnsXII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Kuhns XII similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Kuhns XII similarity

Return type

float

Examples

>>> cmp = KuhnsXII()
>>> cmp.sim('cat', 'hat')
0.2493573264781491
>>> cmp.sim('Niall', 'Neil')
0.1323010752688172
>>> cmp.sim('aluminum', 'Catalan')
0.012877474353417137
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Kuhns XII similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kuhns XII similarity

Return type

float

Examples

>>> cmp = KuhnsXII()
>>> cmp.sim_score('cat', 'hat')
97.0
>>> cmp.sim_score('Niall', 'Neil')
51.266666666666666
>>> cmp.sim_score('aluminum', 'Catalan')
9.902777777777779
>>> cmp.sim_score('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

class abydos.distance.KulczynskiI(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kulczynski I similarity.

For two sets X and Y, Kulczynski I similarity [Kulczynski27] is

\[sim_{KulczynskiI}(X, Y) = \frac{|X \cap Y|}{|X \setminus Y| + |Y \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KulczynskiI} = \frac{a}{b+c}\]

New in version 0.4.0.

Initialize KulczynskiI instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Kulczynski I similarity.

New in version 0.3.6.

sim(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Kulczynski I similarity.

New in version 0.3.6.

sim_score(src, tar)[source]

Return the Kulczynski I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kulczynski I similarity

Return type

float

Examples

>>> cmp = KulczynskiI()
>>> cmp.sim_score('cat', 'hat')
0.5
>>> cmp.sim_score('Niall', 'Neil')
0.2857142857142857
>>> cmp.sim_score('aluminum', 'Catalan')
0.06666666666666667
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.KulczynskiII(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Kulczynski II similarity.

For two sets X and Y, Kulczynski II similarity [Kulczynski27] or Driver & Kroeber similarity [DK32] is

\[sim_{KulczynskiII}(X, Y) = \frac{1}{2} \Bigg(\frac{|X \cap Y|}{|X|} + \frac{|X \cap Y|}{|Y|}\Bigg)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{KulczynskiII} = \frac{1}{2}\Bigg(\frac{a}{a+b}+\frac{a}{a+c}\Bigg)\]

New in version 0.4.0.

Initialize KulczynskiII instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Kulczynski II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Kulczynski II similarity

Return type

float

Examples

>>> cmp = KulczynskiII()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3666666666666667
>>> cmp.sim('aluminum', 'Catalan')
0.11805555555555555
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Lorentzian(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Lorentzian distance.

For two multisets X and Y drawn from an alphabet S, Lorentzian distance is

\[dist_{Lorentzian}(X, Y) = \sum_{i \in S} log(1 + |A_i - B_i|)\]

Notes

No primary source for this measure could be located, but it is included in surveys and catalogues, such as [DD16] and [Cha08].

New in version 0.4.0.

Initialize Lorentzian instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Lorentzian distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Lorentzian distance

Return type

float

Examples

>>> cmp = Lorentzian()
>>> cmp.dist('cat', 'hat')
0.6666666666666667
>>> cmp.dist('Niall', 'Neil')
0.7777777777777778
>>> cmp.dist('aluminum', 'Catalan')
0.9358355851062377
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Lorentzian distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Lorentzian distance

Return type

float

Examples

>>> cmp = Lorentzian()
>>> cmp.dist_abs('cat', 'hat')
2.772588722239781
>>> cmp.dist_abs('Niall', 'Neil')
4.852030263919617
>>> cmp.dist_abs('aluminum', 'Catalan')
10.1095256359474
>>> cmp.dist_abs('ATCG', 'TAGC')
6.931471805599453

New in version 0.4.0.

class abydos.distance.Maarel(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Maarel correlation.

For two sets X and Y and a population N, Maarel correlation [vandMaarel69] is

\[corr_{Maarel}(X, Y) = \frac{2|X \cap Y| - |X \setminus Y| - |Y \setminus X|}{|X| + |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Maarel} = \frac{2a - b - c}{2a + b + c}\]

New in version 0.4.0.

Initialize Maarel instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Maarel correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Maarel correlation

Return type

float

Examples

>>> cmp = Maarel()
>>> cmp.corr('cat', 'hat')
0.0
>>> cmp.corr('Niall', 'Neil')
-0.2727272727272727
>>> cmp.corr('aluminum', 'Catalan')
-0.7647058823529411
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Maarel similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Maarel similarity

Return type

float

Examples

>>> cmp = Maarel()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.11764705882352944
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Morisita(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Morisita index of overlap.

Morisita index of overlap [Mor59], following the description of [Hor66], given two populations X and Y drawn from S species, is:

\[sim_{Morisita}(X, Y) = C_{\lambda} = \frac{2\sum_{i=1}^S x_i y_i}{(\lambda_x + \lambda_y)XY}\]

where

\[X = \sum_{i=1}^S x_i ~~;~~ Y = \sum_{i=1}^S y_i\]
\[\lambda_x = \frac{\sum_{i=1}^S x_i(x_i-1)}{X(X-1)} ~~;~~ \lambda_y = \frac{\sum_{i=1}^S y_i(y_i-1)}{Y(Y-1)}\]

New in version 0.4.1.

Initialize Morisita instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Morisita similarity.

New in version 0.3.6.

sim(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Morisita similarity.

New in version 0.3.6.

sim_score(src, tar)[source]

Return the Morisita similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Morisita similarity

Return type

float

Examples

>>> cmp = Morisita()
>>> cmp.sim_score('cat', 'hat')
0.25
>>> cmp.sim_score('Niall', 'Neil')
0.13333333333333333
>>> cmp.sim_score('aluminum', 'Catalan')
1.0
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.1.

class abydos.distance.Manhattan(alphabet=0, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._minkowski.Minkowski

Manhattan distance.

Manhattan distance is the city-block or taxi-cab distance, equivalent to Minkowski distance in \(L^1\)-space.

New in version 0.3.6.

Initialize Manhattan instance.

Parameters
  • alphabet (collection or int) -- The values or size of the alphabet

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Manhattan distance between two strings.

The normalized Manhattan distance is a distance metric in \(L^1\)-space, normalized to [0, 1].

This is identical to Canberra distance.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

The normalized Manhattan distance

Return type

float

Examples

>>> cmp = Manhattan()
>>> cmp.dist('cat', 'hat')
0.5
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.636363636364
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.692307692308
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar, normalized=False)[source]

Return the Manhattan distance between two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • normalized (bool) -- Normalizes to [0, 1] if True

Returns

The Manhattan distance

Return type

float

Examples

>>> cmp = Manhattan()
>>> cmp.dist_abs('cat', 'hat')
4.0
>>> cmp.dist_abs('Niall', 'Neil')
7.0
>>> cmp.dist_abs('Colin', 'Cuilen')
9.0
>>> cmp.dist_abs('ATCG', 'TAGC')
10.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.manhattan(src, tar, qval=2, normalized=False, alphabet=None)[source]

Return the Manhattan distance between two strings.

This is a wrapper for Manhattan.dist_abs().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • normalized (bool) -- Normalizes to [0, 1] if True

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The Manhattan distance

Return type

float

Examples

>>> manhattan('cat', 'hat')
4.0
>>> manhattan('Niall', 'Neil')
7.0
>>> manhattan('Colin', 'Cuilen')
9.0
>>> manhattan('ATCG', 'TAGC')
10.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Manhattan.dist_abs method instead.

abydos.distance.dist_manhattan(src, tar, qval=2, alphabet=0)[source]

Return the normalized Manhattan distance between two strings.

This is a wrapper for Manhattan.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The normalized Manhattan distance

Return type

float

Examples

>>> dist_manhattan('cat', 'hat')
0.5
>>> round(dist_manhattan('Niall', 'Neil'), 12)
0.636363636364
>>> round(dist_manhattan('Colin', 'Cuilen'), 12)
0.692307692308
>>> dist_manhattan('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Manhattan.dist method instead.

abydos.distance.sim_manhattan(src, tar, qval=2, alphabet=0)[source]

Return the normalized Manhattan similarity of two strings.

This is a wrapper for Manhattan.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The normalized Manhattan similarity

Return type

float

Examples

>>> sim_manhattan('cat', 'hat')
0.5
>>> round(sim_manhattan('Niall', 'Neil'), 12)
0.363636363636
>>> round(sim_manhattan('Colin', 'Cuilen'), 12)
0.307692307692
>>> sim_manhattan('ATCG', 'TAGC')
0.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Manhattan.sim method instead.

class abydos.distance.Michelet(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Michelet similarity.

For two sets X and Y and a population N, Michelet similarity [TCLM88] is

\[sim_{Michelet}(X, Y) = \frac{|X \cap Y|^2}{|X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Michelet} = \frac{a^2}{(a+b)(a+c)}\]

Following [Seq18], this is termed "Michelet", though Turner is most often listed as the first author in papers presenting this measure.

New in version 0.4.0.

Initialize Michelet instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Michelet similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Michelet similarity

Return type

float

Examples

>>> cmp = Michelet()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.13333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.013888888888888888
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Millar(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Millar's binomial deviance dissimilarity.

For two sets X and Y drawn from a population S, Millar's binomial deviance dissimilarity [AM04] is:

\[dist_{Millar}(X, Y) = \sum_{i=0}^{|S|} \frac{1}{x_i+y_i} \bigg\{x_i log(\frac{x_i}{x_i+y_i}) + y_i log(\frac{y_i}{x_i+y_i}) - (x_i+y_i) log(\frac{1}{2})\bigg\}\]

New in version 0.4.1.

Initialize Millar instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Millar dissimilarity.

New in version 0.3.6.

dist_abs(src, tar)[source]

Return Millar's binomial deviance dissimilarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Millar's binomial deviance dissimilarity

Return type

float

Examples

>>> cmp = Millar()
>>> cmp.dist_abs('cat', 'hat')
2.772588722239781
>>> cmp.dist_abs('Niall', 'Neil')
4.852030263919617
>>> cmp.dist_abs('aluminum', 'Catalan')
9.704060527839234
>>> cmp.dist_abs('ATCG', 'TAGC')
6.931471805599453

New in version 0.4.1.

sim(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Millar dissimilarity.

New in version 0.3.6.

class abydos.distance.Minkowski(pval=1, alphabet=0, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Minkowski distance.

The Minkowski distance [Min10] is a distance metric in \(L^p-space\).

New in version 0.3.6.

Initialize Euclidean instance.

Parameters
  • pval (int) -- The \(p\)-value of the \(L^p\)-space

  • alphabet (collection or int) -- The values or size of the alphabet

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return normalized Minkowski distance of two strings.

The normalized Minkowski distance [Min10] is a distance metric in \(L^p\)-space, normalized to [0, 1].

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

The normalized Minkowski distance

Return type

float

Examples

>>> cmp = Minkowski()
>>> cmp.dist('cat', 'hat')
0.5
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.636363636364
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.692307692308
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar, normalized=False)[source]

Return the Minkowski distance (\(L^p\)-norm) of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • normalized (bool) -- Normalizes to [0, 1] if True

Returns

The Minkowski distance

Return type

float

Examples

>>> cmp = Minkowski()
>>> cmp.dist_abs('cat', 'hat')
4.0
>>> cmp.dist_abs('Niall', 'Neil')
7.0
>>> cmp.dist_abs('Colin', 'Cuilen')
9.0
>>> cmp.dist_abs('ATCG', 'TAGC')
10.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.minkowski(src, tar, qval=2, pval=1, normalized=False, alphabet=0)[source]

Return the Minkowski distance (\(L^p\)-norm) of two strings.

This is a wrapper for Minkowski.dist_abs().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • pval (int or float) -- The \(p\)-value of the \(L^p\)-space

  • normalized (bool) -- Normalizes to [0, 1] if True

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The Minkowski distance

Return type

float

Examples

>>> minkowski('cat', 'hat')
4.0
>>> minkowski('Niall', 'Neil')
7.0
>>> minkowski('Colin', 'Cuilen')
9.0
>>> minkowski('ATCG', 'TAGC')
10.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Minkowski.dist_abs method instead.

abydos.distance.dist_minkowski(src, tar, qval=2, pval=1, alphabet=0)[source]

Return normalized Minkowski distance of two strings.

This is a wrapper for Minkowski.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • pval (int or float) -- The \(p\)-value of the \(L^p\)-space

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The normalized Minkowski distance

Return type

float

Examples

>>> dist_minkowski('cat', 'hat')
0.5
>>> round(dist_minkowski('Niall', 'Neil'), 12)
0.636363636364
>>> round(dist_minkowski('Colin', 'Cuilen'), 12)
0.692307692308
>>> dist_minkowski('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Minkowski.dist method instead.

abydos.distance.sim_minkowski(src, tar, qval=2, pval=1, alphabet=0)[source]

Return normalized Minkowski similarity of two strings.

This is a wrapper for Minkowski.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • pval (int or float) -- The \(p\)-value of the \(L^p\)-space

  • alphabet (collection or int) -- The values or size of the alphabet

Returns

The normalized Minkowski similarity

Return type

float

Examples

>>> sim_minkowski('cat', 'hat')
0.5
>>> round(sim_minkowski('Niall', 'Neil'), 12)
0.363636363636
>>> round(sim_minkowski('Colin', 'Cuilen'), 12)
0.307692307692
>>> sim_minkowski('ATCG', 'TAGC')
0.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Minkowski.sim method instead.

class abydos.distance.MASI(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

MASI similarity.

Measuring Agreement on Set-valued Items (MASI) similarity [Pas06] for two sets X and Y is based on Jaccard similarity:

\[sim_{Jaccard}(X, Y) = \frac{|X \cap Y|}{|X \cup Y|}\]
This Jaccard similarity is scaled by a value M, which is:
  • 1 if \(X = Y\)

  • \(\frac{2}{3}\) if \(X \subset Y\) or \(Y \subset X\)

  • \(\frac{1}{3}\) if \(X \cap Y \neq \emptyset\), \(X \setminus Y \neq \emptyset\), and \(Y \setminus X \neq \emptyset\)

  • 0 if \(X \cap Y = \emptyset\)

New in version 0.4.0.

Initialize MASI instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the MASI similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

MASI similarity

Return type

float

Examples

>>> cmp = MASI()
>>> cmp.sim('cat', 'hat')
0.1111111111111111
>>> cmp.sim('Niall', 'Neil')
0.07407407407407407
>>> cmp.sim('aluminum', 'Catalan')
0.020833333333333332
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Matusita(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Matusita distance.

For two multisets X and Y drawn from an alphabet S, Matusita distance [Mat55] is

\[dist_{Matusita}(X, Y) = \sqrt{\sum_{i \in S} \Bigg(\sqrt{\frac{|A_i|}{|A|}} - \sqrt{\frac{|B_i|}{|B|}}\Bigg)^2}\]

New in version 0.4.0.

Initialize Matusita instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Matusita distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Matusita distance

Return type

float

Examples

>>> cmp = Matusita()
>>> cmp.dist('cat', 'hat')
0.707106781186547
>>> cmp.dist('Niall', 'Neil')
0.796775770420944
>>> cmp.dist('aluminum', 'Catalan')
0.939227805062351
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Matusita distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Matusita distance

Return type

float

Examples

>>> cmp = Matusita()
>>> cmp.dist_abs('cat', 'hat')
1.0
>>> cmp.dist_abs('Niall', 'Neil')
1.126811100699571
>>> cmp.dist_abs('aluminum', 'Catalan')
1.3282687000770907
>>> cmp.dist_abs('ATCG', 'TAGC')
1.414213562373095

New in version 0.4.0.

class abydos.distance.MaxwellPilliner(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Maxwell & Pilliner correlation.

For two sets X and Y and a population N, Maxwell & Pilliner correlation [MP68] is

\[corr_{MaxwellPilliner}(X, Y) = \frac{2(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)} {|X| \cdot |N \setminus X| + |Y| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{MaxwellPilliner} = \frac{2(ad-bc)}{(a+b)(c+d)+(a+c)(b+c)}\]

New in version 0.4.0.

Initialize MaxwellPilliner instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Maxwell & Pilliner correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Maxwell & Pilliner correlation

Return type

float

Examples

>>> cmp = MaxwellPilliner()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.35921989956790845
>>> cmp.corr('aluminum', 'Catalan')
0.10803030303030303
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Maxwell & Pilliner similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Maxwell & Pilliner similarity

Return type

float

Examples

>>> cmp = MaxwellPilliner()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6796099497839543
>>> cmp.sim('aluminum', 'Catalan')
0.5540151515151515
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.McConnaughey(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

McConnaughey correlation.

For two sets X and Y, McConnaughey correlation [McC64] is

\[corr_{McConnaughey}(X, Y) = \frac{|X \cap Y|^2 - |X \setminus Y| \cdot |Y \setminus X|} {|X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{McConnaughey} = \frac{a^2-bc}{(a+b)(a+c)}\]

New in version 0.4.0.

Initialize McConnaughey instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the McConnaughey correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

McConnaughey correlation

Return type

float

Examples

>>> cmp = McConnaughey()
>>> cmp.corr('cat', 'hat')
0.0
>>> cmp.corr('Niall', 'Neil')
-0.26666666666666666
>>> cmp.corr('aluminum', 'Catalan')
-0.7638888888888888
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the McConnaughey similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

McConnaughey similarity

Return type

float

Examples

>>> cmp = McConnaughey()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3666666666666667
>>> cmp.sim('aluminum', 'Catalan')
0.11805555555555558
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.McEwenMichael(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

McEwen & Michael correlation.

For two sets X and Y and a population N, the McEwen & Michael correlation [Mic20] is

\[corr_{McEwenMichael}(X, Y) = \frac{4(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)} {(|X \cap Y| + |(N \setminus X) \setminus Y|)^2 + (|X \setminus Y| + |Y \setminus X|)^2}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{McEwenMichael} = \frac{4(ad-bc)}{(a+d)^2+(b+c)^2}\]

New in version 0.4.0.

Initialize Michael instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the McEwen & Michael correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Michael correlation

Return type

float

Examples

>>> cmp = McEwenMichael()
>>> cmp.corr('cat', 'hat')
0.010203544942933782
>>> cmp.corr('Niall', 'Neil')
0.010189175491654217
>>> cmp.corr('aluminum', 'Catalan')
0.0048084299262381456
>>> cmp.corr('ATCG', 'TAGC')
-0.00016689587032858459

New in version 0.4.0.

sim(src, tar)[source]

Return the McEwen & Michael similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Michael similarity

Return type

float

Examples

>>> cmp = McEwenMichael()
>>> cmp.sim('cat', 'hat')
0.5051017724714669
>>> cmp.sim('Niall', 'Neil')
0.5050945877458272
>>> cmp.sim('aluminum', 'Catalan')
0.502404214963119
>>> cmp.sim('ATCG', 'TAGC')
0.4999165520648357

New in version 0.4.0.

class abydos.distance.Mountford(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Mountford similarity.

For two sets X and Y, the Mountford similarity [Mou62] is

\[sim_{Mountford}(X, Y) = \frac{2|X \cap Y|}{2|X|\cdot|Y|-(|X|+|Y|)\cdot|X \cap Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Mountford} = \frac{2a}{2(a+b)(a+c)-(2a+b+c)a}\]

New in version 0.4.0.

Initialize Mountford instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Mountford similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Mountford similarity

Return type

float

Examples

>>> cmp = Mountford()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.10526315789473684
>>> cmp.sim('aluminum', 'Catalan')
0.015748031496062992
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.MutualInformation(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Mutual Information similarity.

For two sets X and Y and a population N, Mutual Information similarity [CGHH91] is

\[sim_{MI}(X, Y) = log_2(\frac{|X \cap Y| \cdot |N|}{|X| \cdot |Y|})\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{MI} = log_2(\frac{an}{(a+b)(a+c)})\]

New in version 0.4.0.

Initialize MutualInformation instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Mutual Information similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Mutual Information similarity

Return type

float

Examples

>>> cmp = MutualInformation()
>>> cmp.sim('cat', 'hat')
0.933609253088981
>>> cmp.sim('Niall', 'Neil')
0.8911684881725231
>>> cmp.sim('aluminum', 'Catalan')
0.7600321183863901
>>> cmp.sim('ATCG', 'TAGC')
0.17522996523538537

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Mutual Information similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Mutual Information similarity

Return type

float

Examples

>>> cmp = MutualInformation()
>>> cmp.sim_score('cat', 'hat')
6.528166795717758
>>> cmp.sim_score('Niall', 'Neil')
5.661433326581222
>>> cmp.sim_score('aluminum', 'Catalan')
3.428560943378589
>>> cmp.sim_score('ATCG', 'TAGC')
-4.700439718141092

New in version 0.4.0.

class abydos.distance.MSContingency(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Mean squared contingency correlation.

For two sets X and Y and a population N, the mean squared contingency correlation [Col49] is

\[corr_{MSContingency}(X, Y) = \frac{\sqrt{2}(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)} {\sqrt{(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)^2 + |X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}}\]

[Hubalek08] and [CCT10] identify this as Cole similarity. Although Cole discusses this correlation, he does not claim to have developed it. Rather, he presents his coefficient of interspecific association as being his own development: Cole.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{MSContingency} = \frac{\sqrt{2}(ad-bc)}{\sqrt{(ad-bc)^2+(a+b)(a+c)(b+d)(c+d)}}\]

New in version 0.4.0.

Initialize MSContingency instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the normalized mean squared contingency corr. of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Mean squared contingency correlation

Return type

float

Examples

>>> cmp = MSContingency()
>>> cmp.corr('cat', 'hat')
0.6298568508557214
>>> cmp.corr('Niall', 'Neil')
0.4798371954796814
>>> cmp.corr('aluminum', 'Catalan')
0.15214891090821628
>>> cmp.corr('ATCG', 'TAGC')
-0.009076921903905553

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized ms contingency similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Mean squared contingency similarity

Return type

float

Examples

>>> cmp = MSContingency()
>>> cmp.sim('cat', 'hat')
0.8149284254278607
>>> cmp.sim('Niall', 'Neil')
0.7399185977398407
>>> cmp.sim('aluminum', 'Catalan')
0.5760744554541082
>>> cmp.sim('ATCG', 'TAGC')
0.49546153904804724

New in version 0.4.0.

class abydos.distance.Overlap(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Overlap coefficient.

For two sets X and Y, the overlap coefficient [Szy34][Sim49], also called the Szymkiewicz-Simpson coefficient and Simpson's ecological coexistence coefficient, is

\[sim_{overlap}(X, Y) = \frac{|X \cap Y|}{min(|X|, |Y|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{overlap} = \frac{a}{min(a+b, a+c)}\]

New in version 0.3.6.

Initialize Overlap instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the overlap coefficient of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Overlap similarity

Return type

float

Examples

>>> cmp = Overlap()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.4
>>> cmp.sim('aluminum', 'Catalan')
0.125
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_overlap(src, tar, qval=2)[source]

Return the overlap distance between two strings.

This is a wrapper for Overlap.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Overlap distance

Return type

float

Examples

>>> dist_overlap('cat', 'hat')
0.5
>>> dist_overlap('Niall', 'Neil')
0.6
>>> dist_overlap('aluminum', 'Catalan')
0.875
>>> dist_overlap('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Overlap.dist method instead.

abydos.distance.sim_overlap(src, tar, qval=2)[source]

Return the overlap coefficient of two strings.

This is a wrapper for Overlap.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

Returns

Overlap similarity

Return type

float

Examples

>>> sim_overlap('cat', 'hat')
0.5
>>> sim_overlap('Niall', 'Neil')
0.4
>>> sim_overlap('aluminum', 'Catalan')
0.125
>>> sim_overlap('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Overlap.sim method instead.

class abydos.distance.Pattern(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Pattern difference.

For two sets X and Y and a population N, the pattern difference [BB95], Batagelj & Bren's \(- bc -\) is

\[dist_{pattern}(X, Y) = \frac{4 \cdot |X \setminus Y| \cdot |Y \setminus X|} {|N|^2}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{pattern} = \frac{4bc}{n^2}\]

In [Cor17], the formula omits the 4 in the numerator: \(\frac{bc}{n^2}\).

New in version 0.4.0.

Initialize Pattern instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Pattern difference of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pattern difference

Return type

float

Examples

>>> cmp = Pattern()
>>> cmp.dist('cat', 'hat')
2.6030820491461892e-05
>>> cmp.dist('Niall', 'Neil')
7.809246147438568e-05
>>> cmp.dist('aluminum', 'Catalan')
0.0003635035904093472
>>> cmp.dist('ATCG', 'TAGC')
0.0001626926280716368

New in version 0.4.0.

class abydos.distance.PearsonHeronII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Pearson & Heron II correlation.

For two sets X and Y and a population N, Pearson & Heron II correlation [PH13] is

\[corr_{PearsonHeronII}(X, Y) = \cos \Big(\frac{\pi\sqrt{|X \setminus Y| \cdot |Y \setminus X|}} {\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + \sqrt{|X \setminus Y| \cdot |Y \setminus X|}}\Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{PearsonHeronII} = \cos \Big(\frac{\pi\sqrt{bc}}{\sqrt{ad}+\sqrt{bc}}\Big)\]

New in version 0.4.0.

Initialize PearsonHeronII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Pearson & Heron II correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson & Heron II correlation

Return type

float

Examples

>>> cmp = PearsonHeronII()
>>> cmp.corr('cat', 'hat')
0.9885309061036239
>>> cmp.corr('Niall', 'Neil')
0.9678978997263907
>>> cmp.corr('aluminum', 'Catalan')
0.7853000893691571
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Pearson & Heron II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson & Heron II similarity

Return type

float

Examples

>>> cmp = PearsonHeronII()
>>> cmp.sim('cat', 'hat')
0.994265453051812
>>> cmp.sim('Niall', 'Neil')
0.9839489498631954
>>> cmp.sim('aluminum', 'Catalan')
0.8926500446845785
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.PearsonII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._pearson_chi_squared.PearsonChiSquared

Pearson II similarity.

For two sets X and Y and a population N, the Pearson II similarity [PH13], Pearson's coefficient of mean square contingency, is

\[corr_{PearsonII} = \sqrt{\frac{\chi^2}{|N|+\chi^2}}\]

where

\[\chi^2 = sim_{PearsonChiSquared}(X, Y) = \frac{|N| \cdot (|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)^2} {|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[\chi^2 = sim_{PearsonChiSquared} = \frac{n \cdot (ad-bc)^2}{(a+b)(a+c)(b+d)(c+d)}\]

New in version 0.4.0.

Initialize PearsonII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Pearson II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Pearson II similarity

Return type

float

Examples

>>> cmp = PearsonII()
>>> cmp.sim('cat', 'hat')
0.6298568508557214
>>> cmp.sim('Niall', 'Neil')
0.47983719547968123
>>> cmp.sim('aluminum', 'Catalan')
0.15214891090821628
>>> cmp.sim('ATCG', 'TAGC')
0.009076921903905551

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Pearson II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson II similarity

Return type

float

Examples

>>> cmp = PearsonII()
>>> cmp.sim_score('cat', 'hat')
0.44537605041688455
>>> cmp.sim_score('Niall', 'Neil')
0.3392961347892176
>>> cmp.sim_score('aluminum', 'Catalan')
0.10758552665334761
>>> cmp.sim_score('ATCG', 'TAGC')
0.006418353030552324

New in version 0.4.0.

class abydos.distance.PearsonIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._pearson_phi.PearsonPhi

Pearson III correlation.

For two sets X and Y and a population N, the Pearson III correlation [PH13], Pearson's coefficient of racial likeness, is

\[corr_{PearsonIII} = \sqrt{\frac{\phi}{|N|+\phi}}\]

where

\[\phi = corr_{PearsonPhi}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {\sqrt{|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[\phi = corr_{PearsonPhi} = \frac{ad-bc} {\sqrt{(a+b)(a+c)(b+c)(b+d)}}\]

New in version 0.4.0.

Initialize PearsonIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Pearson III correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson III correlation

Return type

float

Examples

>>> cmp = PearsonIII()
>>> cmp.corr('cat', 'hat')
0.025180989806958435
>>> cmp.corr('Niall', 'Neil')
0.021444241017487504
>>> cmp.corr('aluminum', 'Catalan')
0.011740218922356615
>>> cmp.corr('ATCG', 'TAGC')
-0.0028612777635371113

New in version 0.4.0.

sim(src, tar)[source]

Return the Pearson III similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson III similarity

Return type

float

Examples

>>> cmp = PearsonIII()
>>> cmp.sim('cat', 'hat')
0.5125904949034792
>>> cmp.sim('Niall', 'Neil')
0.5107221205087438
>>> cmp.sim('aluminum', 'Catalan')
0.5058701094611783
>>> cmp.sim('ATCG', 'TAGC')
0.49856936111823147

New in version 0.4.0.

class abydos.distance.PearsonChiSquared(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Pearson's Chi-Squared similarity.

For two sets X and Y and a population N, the Pearson's \(\chi^2\) similarity [PH13] is

\[sim_{PearsonChiSquared}(X, Y) = \frac{|N| \cdot (|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)^2} {|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}\]

This is also Pearson I similarity.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{PearsonChiSquared} = \frac{n(ad-bc)^2}{(a+b)(a+c)(b+d)(c+d)}\]

New in version 0.4.0.

Initialize PearsonChiSquared instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return Pearson's Chi-Squared correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson's Chi-Squared correlation

Return type

float

Examples

>>> cmp = PearsonChiSquared()
>>> cmp.corr('cat', 'hat')
0.2474424720578567
>>> cmp.corr('Niall', 'Neil')
0.1300991207720222
>>> cmp.corr('aluminum', 'Catalan')
0.011710186806836291
>>> cmp.corr('ATCG', 'TAGC')
-4.1196952743799446e-05

New in version 0.4.0.

sim(src, tar)[source]

Return Pearson's normalized Chi-Squared similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Pearson's Chi-Squared similarity

Return type

float

Examples

>>> cmp = PearsonChiSquared()
>>> cmp.corr('cat', 'hat')
0.2474424720578567
>>> cmp.corr('Niall', 'Neil')
0.1300991207720222
>>> cmp.corr('aluminum', 'Catalan')
0.011710186806836291
>>> cmp.corr('ATCG', 'TAGC')
-4.1196952743799446e-05

New in version 0.4.0.

sim_score(src, tar)[source]

Return Pearson's Chi-Squared similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson's Chi-Squared similarity

Return type

float

Examples

>>> cmp = PearsonChiSquared()
>>> cmp.sim_score('cat', 'hat')
193.99489809335964
>>> cmp.sim_score('Niall', 'Neil')
101.99771068526542
>>> cmp.sim_score('aluminum', 'Catalan')
9.19249664336649
>>> cmp.sim_score('ATCG', 'TAGC')
0.032298410951138765

New in version 0.4.0.

class abydos.distance.PearsonPhi(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Pearson's Phi correlation.

For two sets X and Y and a population N, the Pearson's \(\phi\) correlation [Pea00][PH13][Guirk] is

\[corr_{PearsonPhi}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {\sqrt{|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}}\]

This is also Pearson & Heron I similarity.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{PearsonPhi} = \frac{ad-bc} {\sqrt{(a+b)(a+c)(b+d)(c+d)}}\]

Notes

In terms of a confusion matrix, this is equivalent to the Matthews correlation coefficient ConfusionTable.mcc().

New in version 0.4.0.

Initialize PearsonPhi instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return Pearson's Phi correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson's Phi correlation

Return type

float

Examples

>>> cmp = PearsonPhi()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.36069255713421955
>>> cmp.corr('aluminum', 'Catalan')
0.10821361655002706
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Pearson's Phi similarity of two strings.

This is normalized to [0, 1] by adding 1 and dividing by 2.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Pearson's Phi similarity

Return type

float

Examples

>>> cmp = PearsonPhi()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6803462785671097
>>> cmp.sim('aluminum', 'Catalan')
0.5541068082750136
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.Peirce(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Peirce correlation.

For two sets X and Y and a population N, the Peirce correlation [Pei84] is

\[corr_{Peirce}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus Y|} {|X| \cdot |N \setminus X|}\]

Both [CCT10] and [Hubalek08] present a different formula and incorrectly attribute it to Peirce. Likewise, [Doo84] presents a different formula and incorrectly attributes it to Peirce. This is distinct from the formula he presents and attributes to himself.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Peirce} = \frac{ad-bc}{(a+b)(c+d)}\]

New in version 0.4.0.

Initialize Peirce instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Peirce correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Peirce correlation

Return type

float

Examples

>>> cmp = Peirce()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.32947729220222793
>>> cmp.corr('aluminum', 'Catalan')
0.10209049255441008
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Peirce similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Peirce similarity

Return type

float

Examples

>>> cmp = Peirce()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.664738646101114
>>> cmp.sim('aluminum', 'Catalan')
0.5510452462772051
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.QGram(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

q-gram distance.

For two multisets X and Y, q-gram distance [Ukk92] is

\[sim_{QGram}(X, Y) = |X \triangle Y|\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{QGram} = b+c\]

Notes

This class uses bigrams without appended start or stop symbols, by default, as in [Ukk92]'s examples. It is described as the \(L_1\) norm of the difference of two strings' q-gram profiles, which are the vectors of q-gram occurrences. But this norm is simply the symmetric difference of the two multisets.

There aren't any limitations on which tokenizer is used with this class, but, as the name would imply, q-grams are expected and the default.

The normalized form uses the union of X and Y, making it equivalent to the Jaccard distance Jaccard, but the Jaccard class, by default uses bigrams with start & stop symbols.

New in version 0.4.0.

Initialize QGram instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized q-gram distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

q-gram distance

Return type

float

Examples

>>> cmp = QGram()
>>> cmp.sim('cat', 'hat')
0.33333333333333337
>>> cmp.sim('Niall', 'Neil')
0.0
>>> cmp.sim('aluminum', 'Catalan')
0.08333333333333337
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the q-gram distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

q-gram distance

Return type

int

Examples

>>> cmp = QGram()
>>> cmp.dist_abs('cat', 'hat')
2
>>> cmp.dist_abs('Niall', 'Neil')
7
>>> cmp.dist_abs('aluminum', 'Catalan')
11
>>> cmp.dist_abs('ATCG', 'TAGC')
6
>>> cmp.dist_abs('01000', '001111')
5

New in version 0.4.0.

class abydos.distance.RaupCrick(**kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Raup-Crick similarity.

For two sets X and Y and a population N, Raup-Crick similarity [RC79] is:

Notes

Observe that Raup-Crick similarity is related to Henderson-Heron similarity in that the former is the sum of all Henderson-Heron similarities for an intersection size ranging from 0 to the true intersection size.

New in version 0.4.1.

Initialize RaupCrick instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

sim(src, tar)[source]

Return the Raup-Crick similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Raup-Crick similarity

Return type

float

Examples

>>> cmp = RaupCrick()
>>> cmp.sim('cat', 'hat')
0.9999998002120004
>>> cmp.sim('Niall', 'Neil')
0.9999975146378747
>>> cmp.sim('aluminum', 'Catalan')
0.9968397599851411
>>> cmp.sim('ATCG', 'TAGC')
0.9684367974410505

New in version 0.4.1.

class abydos.distance.ReesLevenshtein(block_limit=2, normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Rees-Levenshtein distance.

Rees-Levenshtein distance [Ree14][RB13] is the "Modified Damerau-Levenshtein Distance Algorithm, created by Tony Rees as part of Taxamatch.

New in version 0.4.0.

Initialize ReesLevenshtein instance.

Parameters
  • block_limit (int) -- The block length limit

  • normalizer (function) -- A function that takes an list and computes a normalization term by which the edit distance is divided (max by default). Another good option is the sum function.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Rees-Levenshtein distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Rees-Levenshtein distance

Return type

float

Examples

>>> cmp = ReesLevenshtein()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.6
>>> cmp.dist('aluminum', 'Catalan')
0.875
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Rees-Levenshtein distance of two strings.

This is a straightforward port of the PL/SQL implementation at https://confluence.csiro.au/public/taxamatch/the-mdld-modified-damerau-levenshtein-distance-algorithm

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Rees-Levenshtein distance

Return type

float

Examples

>>> cmp = ReesLevenshtein()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
3
>>> cmp.dist_abs('aluminum', 'Catalan')
7
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.4.0.

class abydos.distance.RogersTanimoto(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Rogers & Tanimoto similarity.

For two sets X and Y and a population N, the Rogers-Tanimoto similarity [RT60] is

\[sim_{RogersTanimoto}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|} {|X \setminus Y| + |Y \setminus X| + |N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{RogersTanimoto} = \frac{a+d}{b+c+n}\]

New in version 0.4.0.

Initialize RogersTanimoto instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Rogers & Tanimoto similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Rogers & Tanimoto similarity

Return type

float

Examples

>>> cmp = RogersTanimoto()
>>> cmp.sim('cat', 'hat')
0.9898477157360406
>>> cmp.sim('Niall', 'Neil')
0.9823008849557522
>>> cmp.sim('aluminum', 'Catalan')
0.9625
>>> cmp.sim('ATCG', 'TAGC')
0.9748110831234257

New in version 0.4.0.

class abydos.distance.RogotGoldberg(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Rogot & Goldberg similarity.

For two sets X and Y and a population N, Rogot & Goldberg's "second index adjusted agreement" \(A_2\) [RG66] is

\[sim_{RogotGoldberg}(X, Y) = \frac{1}{2}\Bigg( \frac{2|X \cap Y|}{|X|+|Y|} + \frac{2|(N \setminus X) \setminus Y|} {|N \setminus X|+|N \setminus Y|} \Bigg)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{RogotGoldberg} = \frac{1}{2}\Bigg( \frac{2a}{2a+b+c} + \frac{2d}{2d+b+c} \Bigg)\]

New in version 0.4.0.

Initialize RogotGoldberg instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Rogot & Goldberg similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Rogot & Goldberg similarity

Return type

float

Examples

>>> cmp = RogotGoldberg()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6795702691656449
>>> cmp.sim('aluminum', 'Catalan')
0.5539941668876179
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.RussellRao(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Russell & Rao similarity.

For two sets X and Y and a population N, the Russell & Rao similarity [RR40] is

\[sim_{RussellRao}(X, Y) = \frac{|X \cap Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{RussellRao} = \frac{a}{n}\]

New in version 0.4.0.

Initialize RussellRao instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Russell & Rao similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Russell & Rao similarity

Return type

float

Examples

>>> cmp = RussellRao()
>>> cmp.sim('cat', 'hat')
0.002551020408163265
>>> cmp.sim('Niall', 'Neil')
0.002551020408163265
>>> cmp.sim('aluminum', 'Catalan')
0.0012738853503184713
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.ScottPi(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Scott's Pi correlation.

For two sets X and Y and a population N, Scott's \(\pi\) correlation [Sco55] is

\[corr_{Scott_\pi}(X, Y) = \pi = \frac{p_o - p_e^\pi}{1 - p_e^\pi}\]

where

\[ \begin{align}\begin{aligned}\begin{array}{ll} p_o &= \frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}\\p_e^\pi &= \Big(\frac{|X| + |Y|}{2 \cdot |N|}\Big)^2 + \Big(\frac{|N \setminus X| + |N \setminus Y|}{2 \cdot |N|}\Big)^2 \end{array}\end{aligned}\end{align} \]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[ \begin{align}\begin{aligned}\begin{array}{ll} p_o &= \frac{a+d}{n}\\p_e^\pi &= \Big(\frac{2a+b+c}{2n}\Big)^2 + \Big(\frac{2d+b+c}{2n}\Big)^2 \end{array}\end{aligned}\end{align} \]

New in version 0.4.0.

Initialize ScottPi instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Scott's Pi correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Scott's Pi correlation

Return type

float

Examples

>>> cmp = ScottPi()
>>> cmp.corr('cat', 'hat')
0.49743589743589733
>>> cmp.corr('Niall', 'Neil')
0.35914053833129245
>>> cmp.corr('aluminum', 'Catalan')
0.10798833377524023
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237489689

New in version 0.4.0.

sim(src, tar)[source]

Return the Scott's Pi similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Scott's Pi similarity

Return type

float

Examples

>>> cmp = ScottPi()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6795702691656462
>>> cmp.sim('aluminum', 'Catalan')
0.5539941668876202
>>> cmp.sim('ATCG', 'TAGC')
0.49679075738125517

New in version 0.4.0.

class abydos.distance.Shape(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Penrose's shape difference.

For two sets X and Y and a population N, the Penrose's shape difference [Pen52] is

\[dist_{Shape}(X, Y) = \frac{1}{|N|}\cdot\Big(\sum_{x \in (X \triangle Y)} x^2\Big) - \Big(\frac{|X \triangle Y|}{|N|}\Big)^2\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Shape} = \frac{1}{n}\Big(\sum_{x \in b} x^2 + \sum_{x \in c} x^2\Big) - \Big(\frac{b+c}{n}\Big)^2\]

In [Cor17], the formula is instead \(\frac{n(b+c)-(b-c)^2}{n^2}\), but it is clear from [Pen52] that this should not be an assymmetric value with respect to the ordering of the two sets, among other errors in this formula. Meanwhile, [DD16] gives the formula \(\sqrt{\sum((x_i-\bar{x})-(y_i-\bar{y}))^2}\).

New in version 0.4.0.

Initialize Shape instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Penrose's shape difference of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Shape ifference

Return type

float

Examples

>>> cmp = Shape()
>>> cmp.sim('cat', 'hat')
0.994923990004165
>>> cmp.sim('Niall', 'Neil')
0.9911511479591837
>>> cmp.sim('aluminum', 'Catalan')
0.9787090754188811
>>> cmp.sim('ATCG', 'TAGC')
0.9874075905872554

New in version 0.4.0.

class abydos.distance.Size(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Penrose's size difference.

For two sets X and Y and a population N, the Penrose's size difference [Pen52] is

\[sim_{Size}(X, Y) = \frac{(|X \triangle Y|)^2}{|N|^2}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Size} = \frac{(b+c)^2}{n^2}\]

In [Cor17], the formula is instead \(\frac{(b-c)^2}{n^2}\), but it is clear from [Pen52] that this should not be an assymmetric value with respect two the ordering of the two sets. Meanwhile, [DD16] gives a formula that is equivalent to \(\sqrt{n}\cdot(b+c)\).

New in version 0.4.0.

Initialize Size instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the Penrose's size difference of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Size difference

Return type

float

Examples

>>> cmp = Size()
>>> cmp.sim('cat', 'hat')
0.9999739691795085
>>> cmp.sim('Niall', 'Neil')
0.9999202806122449
>>> cmp.sim('aluminum', 'Catalan')
0.9996348736257049
>>> cmp.sim('ATCG', 'TAGC')
0.9998373073719283

New in version 0.4.0.

class abydos.distance.SokalMichener(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sokal & Michener similarity.

For two sets X and Y and a population N, the Sokal & Michener's simple matching coefficient [SM58], equivalent to the Rand index [Ran71] is

\[sim_{SokalMichener}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{SokalMichener} = \frac{a+d}{n}\]

Notes

The associated distance metric is the mean Manhattan distance and 4 times the value of the variance dissimilarity of [Cor17].

In terms of a confusion matrix, this is equivalent to accuracy ConfusionTable.accuracy().

New in version 0.4.0.

Initialize SokalMichener instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sokal & Michener similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sokal & Michener similarity

Return type

float

Examples

>>> cmp = SokalMichener()
>>> cmp.sim('cat', 'hat')
0.9948979591836735
>>> cmp.sim('Niall', 'Neil')
0.9910714285714286
>>> cmp.sim('aluminum', 'Catalan')
0.9808917197452229
>>> cmp.sim('ATCG', 'TAGC')
0.9872448979591837

New in version 0.4.0.

class abydos.distance.SokalSneathI(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sokal & Sneath I similarity.

For two sets X and Y and a population N, Sokal & Sneath I similarity [SS63] is

\[sim_{SokalSneathI}(X, Y) = \frac{2(|X \cap Y| + |(N \setminus X) \setminus Y|)} {|X \cap Y| + |(N \setminus X) \setminus Y| + |N|}\]

This is the first of five "Unnamed coefficients" presented in [SS63]. It corresponds to the "Matched pairs carry twice the weight of unmatched pairs in the Denominator" with "Negative Matches in Numerator Included". "Negative Matches in Numerator Excluded" corresponds to the Sørensen–Dice coefficient, Dice.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{SokalSneathI} = \frac{2(a+d)}{a+d+n}\]

New in version 0.4.0.

Initialize SokalSneathI instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sokal & Sneath I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sokal & Sneath I similarity

Return type

float

Examples

>>> cmp = SokalSneathI()
>>> cmp.sim('cat', 'hat')
0.9974424552429667
>>> cmp.sim('Niall', 'Neil')
0.9955156950672646
>>> cmp.sim('aluminum', 'Catalan')
0.9903536977491961
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516

New in version 0.4.0.

class abydos.distance.SokalSneathII(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sokal & Sneath II similarity.

For two sets X and Y, Sokal & Sneath II similarity [SS63] is

\[sim_{SokalSneathII}(X, Y) = \frac{|X \cap Y|} {|X \cap Y| + 2|X \triangle Y|}\]

This is the second of five "Unnamed coefficients" presented in [SS63]. It corresponds to the "Unmatched pairs carry twice the weight of matched pairs in the Denominator" with "Negative Matches in Numerator Excluded". "Negative Matches in Numerator Included" corresponds to the Rogers & Tanimoto similarity, RogersTanimoto.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{SokalSneathII} = \frac{a}{a+2(b+c)}\]

New in version 0.4.0.

Initialize SokalSneathII instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sokal & Sneath II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sokal & Sneath II similarity

Return type

float

Examples

>>> cmp = SokalSneathII()
>>> cmp.sim('cat', 'hat')
0.2
>>> cmp.sim('Niall', 'Neil')
0.125
>>> cmp.sim('aluminum', 'Catalan')
0.03225806451612903
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.SokalSneathIII(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sokal & Sneath III similarity.

For two sets X and Y and a population N, Sokal & Sneath III similarity [SS63] is

\[sim_{SokalSneathIII}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|} {|X \triangle Y|}\]

This is the third of five "Unnamed coefficients" presented in [SS63]. It corresponds to the "Unmatched pairs only in the Denominator" with "Negative Matches in Numerator Excluded". "Negative Matches in Numerator Included" corresponds to the Kulczynski I coefficient, KulczynskiI.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{SokalSneathIII} = \frac{a+d}{b+c}\]

New in version 0.4.0.

Initialize SokalSneathIII instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Sokal & Sneath III similarity.

New in version 0.3.6.

sim(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Sokal & Sneath III similarity.

New in version 0.3.6.

sim_score(src, tar)[source]

Return the Sokal & Sneath III similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sokal & Sneath III similarity

Return type

float

Examples

>>> cmp = SokalSneathIII()
>>> cmp.sim_score('cat', 'hat')
195.0
>>> cmp.sim_score('Niall', 'Neil')
111.0
>>> cmp.sim_score('aluminum', 'Catalan')
51.333333333333336
>>> cmp.sim_score('ATCG', 'TAGC')
77.4

New in version 0.4.0.

class abydos.distance.SokalSneathIV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sokal & Sneath IV similarity.

For two sets X and Y and a population N, Sokal & Sneath IV similarity [SS63] is

\[sim_{SokalSneathIV}(X, Y) = \frac{1}{4}\Bigg( \frac{|X \cap Y|}{|X|}+ \frac{|X \cap Y|}{|Y|}+ \frac{|(N \setminus X) \setminus Y|} {|N \setminus Y|}+ \frac{|(N \setminus X) \setminus Y|} {|N \setminus X|} \Bigg)\]

This is the fourth of five "Unnamed coefficients" presented in [SS63]. It corresponds to the first "Marginal totals in the Denominator" with "Negative Matches in Numerator Included". "Negative Matches in Numerator Excluded" corresponds to the Kulczynski II similarity, KulczynskiII. This is also Rogot & Goldberg's "adjusted agreement" \(A_1\) [RG66].

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{SokalSneathIV} = \frac{1}{4}\Big(\frac{a}{a+b}+\frac{a}{a+c}+ \frac{d}{b+d}+\frac{d}{c+d}\Big)\]

New in version 0.4.0.

Initialize SokalSneathIV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sokal & Sneath IV similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sokal & Sneath IV similarity

Return type

float

Examples

>>> cmp = SokalSneathIV()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6810856260030602
>>> cmp.sim('aluminum', 'Catalan')
0.5541986205645999
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.SokalSneathV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sokal & Sneath V similarity.

For two sets X and Y and a population N, Sokal & Sneath V similarity [SS63] is

\[sim_{SokalSneathV}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} {\sqrt{|X| \cdot |Y| \cdot |N \setminus Y| \cdot |N \setminus X|}}\]

This is the fifth of five "Unnamed coefficients" presented in [SS63]. It corresponds to the second "Marginal totals in the Denominator" with "Negative Matches in Numerator Included", also sometimes referred to as Ochiai II similarity. "Negative Matches in Numerator Excluded" corresponds to the Cosine similarity, Cosine.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{SokalSneathV} = \frac{ad}{\sqrt{(a+b)(a+c)(b+d)(c+d)}}\]

New in version 0.4.0.

Initialize SokalSneathV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sokal & Sneath V similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sokal & Sneath V similarity

Return type

float

Examples

>>> cmp = SokalSneathV()
>>> cmp.sim('cat', 'hat')
0.4987179487179487
>>> cmp.sim('Niall', 'Neil')
0.3635068033537323
>>> cmp.sim('aluminum', 'Catalan')
0.11671286273067434
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Sorgenfrei(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Sorgenfrei similarity.

For two sets X and Y, Sorgenfrei similarity [Sor58] is

\[sim_{Sorgenfrei}(X, Y) = \frac{|X \cap Y|^2}{|X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Sorgenfrei} = \frac{a^2}{(a+b)(a+c)}\]

New in version 0.4.0.

Initialize Sorgenfrei instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Sorgenfrei similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Sorgenfrei similarity

Return type

float

Examples

>>> cmp = Sorgenfrei()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.13333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.013888888888888888
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Steffensen(alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Steffensen similarity.

For two sets X and Y and a population N, Steffensen similarity \(\psi^2\) [Ste34] is

\[\begin{split}\begin{array}{ll} sim_{Steffensen_{\psi}}(X, Y) = \psi^2 &= \sum_{i \in X}\sum_{j \in Y} p_{ij} \phi_{ij}^2 \\ \\ \phi_{ij}^2 &= \frac{(p_{ij} - p_{i*}p_{*i})^2} {p_{i*}(1-p_{i*})p_{*j}(1-p_{*j})} \end{array}\end{split}\]

Where each value \(p_{ij}\) is drawn from the 2x2 contingency table:

\(x \in\) tar

\(x \notin\) tar

\(x \in\) src

\(p_{11} = a\)

\(p_{10} = b\)

\(p_{1*} = a+b\)

\(x \notin\) src

\(p_{01} = c\)

\(p_{00} = d\)

\(p_{0*} = c+d\)

\(p_{*1} = a+c\)

\(p_{*0} = b+d\)

\(1\)

New in version 0.4.0.

Initialize Steffensen instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • normalizer (str) -- Specifies the normalization type. See normalizer description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Steffensen similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Steffensen similarity

Return type

float

Examples

>>> cmp = Steffensen()
>>> cmp.sim('cat', 'hat')
0.24744247205786737
>>> cmp.sim('Niall', 'Neil')
0.1300991207720166
>>> cmp.sim('aluminum', 'Catalan')
0.011710186806836031
>>> cmp.sim('ATCG', 'TAGC')
4.1196952743871653e-05

New in version 0.4.0.

class abydos.distance.Stiles(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Stiles similarity.

For two sets X and Y and a population N, Stiles similarity [Sti61] is

\[sim_{Stiles}(X, Y) = log_{10} \frac{|N| \Big(||X \cap Y| \cdot |N| - |X \setminus Y| \cdot |Y \setminus X|| - \frac{|N|}{2}\Big)^2} {|X \setminus Y| \cdot |Y \setminus X| \cdot (|N| - |X \setminus Y|) \cdot (|N| - |Y \setminus X|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Stiles} = log_{10} \frac{n(|an-bc|-\frac{1}{2}n)^2}{bc(n-b)(n-c)}\]

New in version 0.4.0.

Initialize Stiles instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Stiles correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Stiles correlation

Return type

float

Examples

>>> cmp = Stiles()
>>> cmp.corr('cat', 'hat')
0.14701542182970487
>>> cmp.corr('Niall', 'Neil')
0.11767566062554877
>>> cmp.corr('aluminum', 'Catalan')
0.022355640924908403
>>> cmp.corr('ATCG', 'TAGC')
-0.046296656196428934

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Stiles similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Stiles similarity

Return type

float

Examples

>>> cmp = Stiles()
>>> cmp.sim('cat', 'hat')
0.5735077109148524
>>> cmp.sim('Niall', 'Neil')
0.5588378303127743
>>> cmp.sim('aluminum', 'Catalan')
0.5111778204624542
>>> cmp.sim('ATCG', 'TAGC')
0.4768516719017855

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Stiles similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Stiles similarity

Return type

float

Examples

>>> cmp = Stiles()
>>> cmp.sim_score('cat', 'hat')
2.6436977886009236
>>> cmp.sim_score('Niall', 'Neil')
2.1622951406967723
>>> cmp.sim_score('aluminum', 'Catalan')
0.41925115106844024
>>> cmp.sim_score('ATCG', 'TAGC')
-0.8426334527850912

New in version 0.4.0.

class abydos.distance.StuartTau(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Stuart's Tau correlation.

For two sets X and Y and a population N, Stuart's Tau-C correlation [Stu53] is

\[corr_{Stuart_{\tau_c}}(X, Y) = \frac{4 \cdot (|X \cap Y| + |(N \setminus X) \setminus Y| - |X \triangle Y|)}{|N|^2}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Stuart_{\tau_c}} = \frac{4 \cdot ((a+d)-(b+c))}{n^2}\]

New in version 0.4.0.

Initialize StuartTau instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Stuart's Tau correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Stuart's Tau correlation

Return type

float

Examples

>>> cmp = StuartTau()
>>> cmp.corr('cat', 'hat')
0.005049979175343606
>>> cmp.corr('Niall', 'Neil')
0.005010932944606414
>>> cmp.corr('aluminum', 'Catalan')
0.004900807334983164
>>> cmp.corr('ATCG', 'TAGC')
0.0049718867138692216

New in version 0.4.0.

sim(src, tar)[source]

Return the Stuart's Tau similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Stuart's Tau similarity

Return type

float

Examples

>>> cmp = StuartTau()
>>> cmp.sim('cat', 'hat')
0.5025249895876718
>>> cmp.sim('Niall', 'Neil')
0.5025054664723032
>>> cmp.sim('aluminum', 'Catalan')
0.5024504036674916
>>> cmp.sim('ATCG', 'TAGC')
0.5024859433569346

New in version 0.4.0.

class abydos.distance.Tarantula(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tarantula similarity.

For two sets X and Y and a population N, Tarantula similarity [JH05] is

\[sim_{Tarantula}(X, Y) = \frac{\frac{|X \cap Y|}{|X \cap Y| + |X \setminus Y|}} {\frac{|X \cap Y|}{|X \cap Y| + |X \setminus Y|} + \frac{|Y \setminus X|} {|Y \setminus X| + |(N \setminus X) \setminus Y|}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Tarantula} = \frac{\frac{a}{a+b}}{\frac{a}{a+b} + \frac{c}{c+d}}\]

New in version 0.4.0.

Initialize Tarantula instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Tarantula similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tarantula similarity

Return type

float

Examples

>>> cmp = Tarantula()
>>> cmp.sim('cat', 'hat')
0.9948979591836735
>>> cmp.sim('Niall', 'Neil')
0.98856416772554
>>> cmp.sim('aluminum', 'Catalan')
0.9249106078665077
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Tarwid(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tarwid correlation.

For two sets X and Y and a population N, the Tarwid correlation [Tar60] is

\[corr_{Tarwid}(X, Y) = \frac{|N| \cdot |X \cap Y| - |X| \cdot |Y|} {|N| \cdot |X \cap Y| + |X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Tarwid} = \frac{na-(a+b)(a+c)}{na+(a+b)(a+c)}\]

New in version 0.4.0.

Initialize Tarwid instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Tarwid correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tarwid correlation

Return type

float

Examples

>>> cmp = Tarwid()
>>> cmp.corr('cat', 'hat')
0.9797979797979798
>>> cmp.corr('Niall', 'Neil')
0.9624530663329162
>>> cmp.corr('aluminum', 'Catalan')
0.8319719953325554
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Tarwid similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tarwid similarity

Return type

float

Examples

>>> cmp = Tarwid()
>>> cmp.sim('cat', 'hat')
0.9898989898989898
>>> cmp.sim('Niall', 'Neil')
0.981226533166458
>>> cmp.sim('aluminum', 'Catalan')
0.9159859976662776
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Tetrachoric(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tetrachoric correlation coefficient.

For two sets X and Y and a population N, the Tetrachoric correlation coefficient [Pea00] is

\[corr_{Tetrachoric}(X, Y) = \cos \Big(\frac{\pi \sqrt{|X \setminus Y| \cdot |Y \setminus X|}} {\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + \sqrt{|X \setminus Y| \cdot |Y \setminus X|}}\Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Tetrachoric} = \cos \frac{\pi\sqrt{bc}}{\sqrt{ad}+\sqrt{bc}}\]

New in version 0.4.0.

Initialize Tetrachoric instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Tetrachoric correlation coefficient of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tetrachoric correlation coefficient

Return type

float

Examples

>>> cmp = Tetrachoric()
>>> cmp.corr('cat', 'hat')
0.9885309061036239
>>> cmp.corr('Niall', 'Neil')
0.9678978997263907
>>> cmp.corr('aluminum', 'Catalan')
0.7853000893691571
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Tetrachoric correlation coefficient of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tetrachoric correlation coefficient

Return type

float

Examples

>>> cmp = Tetrachoric()
>>> cmp.sim('cat', 'hat')
0.994265453051812
>>> cmp.sim('Niall', 'Neil')
0.9839489498631954
>>> cmp.sim('aluminum', 'Catalan')
0.8926500446845785
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.TullossR(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tulloss' R similarity.

For two sets X and Y and a population N, Tulloss' R similarity [Tul97] is

\[sim_{Tulloss_R}(X, Y) = \frac{log(1+\frac{|X \cap Y|}{|X|}) \cdot log(1+\frac{|X \cap Y|} {|Y|})}{log^2(2)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Tulloss_R} = \frac{log(1+\frac{a}{a+b}) \cdot log(1+\frac{a}{a+c})}{log^2(2)}\]

New in version 0.4.0.

Initialize TullossR instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Tulloss' R similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tulloss' R similarity

Return type

float

Examples

>>> cmp = TullossR()
>>> cmp.sim('cat', 'hat')
0.34218112724994865
>>> cmp.sim('Niall', 'Neil')
0.2014703364316006
>>> cmp.sim('aluminum', 'Catalan')
0.025829125872886074
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.TullossS(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tulloss' S similarity.

For two sets X and Y and a population N, Tulloss' S similarity [Tul97] is

\[sim_{Tulloss_S}(X, Y) = \frac{1}{\sqrt{log_2(2+\frac{min(|X \setminus Y|, |Y \setminus X|)} {|X \cap Y|+1})}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Tulloss_S} = \frac{1}{\sqrt{log_2(2+\frac{min(b,c)}{a+1})}}\]

New in version 0.4.0.

Initialize TullossS instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Tulloss' S similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tulloss' S similarity

Return type

float

Examples

>>> cmp = TullossS()
>>> cmp.sim('cat', 'hat')
0.8406515643305636
>>> cmp.sim('Niall', 'Neil')
0.7943108670863427
>>> cmp.sim('aluminum', 'Catalan')
0.6376503816669968
>>> cmp.sim('ATCG', 'TAGC')
0.5968309535438173

New in version 0.4.0.

class abydos.distance.TullossT(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tulloss' T similarity.

For two sets X and Y and a population N, Tulloss' T similarity [Tul97] is

\[ \begin{align}\begin{aligned}\begin{array}{l} sim_{Tulloss_T}(X, Y) = \sqrt{sim_{Tulloss_U}(X, Y) \cdot sim_{Tulloss_S}(X, Y) \cdot sim_{Tulloss_R}(X, Y)}\\= \sqrt{ log_2(1+\frac{min(|X \setminus Y|, |Y \setminus X|)+|X \cap Y|} {max(|X \setminus Y|, |Y \setminus X|)+|X \cap Y|}) \cdot \frac{1}{\sqrt{log_2(2+\frac{min(|X \setminus Y|, |Y \setminus X|)} {|X \cap Y|+1})}} \cdot \frac{log(1+\frac{|X \cap Y|}{|X|}) \cdot log(1+\frac{|X \cap Y|} {|Y|})}{log^2(2)}} \end{array}\end{aligned}\end{align} \]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Tulloss_T} = \sqrt{ log_2\Big(1+\frac{min(b, c)+a}{max(b, c)+a}\Big) \cdot \frac{1}{\sqrt{log_2(2+\frac{min(b,c)}{a+1})}} \cdot \frac{log(1+\frac{a}{a+b}) \cdot log(1+\frac{a}{a+c})}{log^2(2)}}\]

New in version 0.4.0.

Initialize TullossT instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Tulloss' T similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tulloss' T similarity

Return type

float

Examples

>>> cmp = TullossT()
>>> cmp.sim('cat', 'hat')
0.5363348766461724
>>> cmp.sim('Niall', 'Neil')
0.3740873705689327
>>> cmp.sim('aluminum', 'Catalan')
0.1229300783095269
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.TullossU(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tulloss' U similarity.

For two sets X and Y, Tulloss' U similarity [Tul97] is

\[sim_{Tulloss_U}(X, Y) = log_2\Big(1+\frac{min(|X \setminus Y|, |Y \setminus X|)+|X \cap Y|} {max(|X \setminus Y|, |Y \setminus X|)+|X \cap Y|}\Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Tulloss_U} = log_2\Big(1+\frac{min(b, c)+a}{max(b, c)+a}\Big)\]

New in version 0.4.0.

Initialize TullossU instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Tulloss' U similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tulloss' U similarity

Return type

float

Examples

>>> cmp = TullossU()
>>> cmp.sim('cat', 'hat')
1.0
>>> cmp.sim('Niall', 'Neil')
0.8744691179161412
>>> cmp.sim('aluminum', 'Catalan')
0.917537839808027
>>> cmp.sim('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.Tversky(alpha=1.0, beta=1.0, bias=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Tversky index.

The Tversky index [Tve77] is defined as: For two sets X and Y:

\[sim_{Tversky}(X, Y) = \frac{|X \cap Y|} {|X \cap Y| + \alpha|X - Y| + \beta|Y - X|}\]

\(\alpha = \beta = 1\) is equivalent to the Jaccard & Tanimoto similarity coefficients.

\(\alpha = \beta = 0.5\) is equivalent to the Sørensen-Dice similarity coefficient [Dic45][Sorensen48].

Unequal α and β will tend to emphasize one or the other set's contributions:

  • \(\alpha > \beta\) emphasizes the contributions of X over Y

  • \(\alpha < \beta\) emphasizes the contributions of Y over X)

Parameter values' relation to 1 emphasizes different types of contributions:

  • \(\alpha\) and \(\beta > 1\) emphsize unique contributions over the intersection

  • \(\alpha\) and \(\beta < 1\) emphsize the intersection over unique contributions

The symmetric variant is defined in [JBG13]. This is activated by specifying a bias parameter.

New in version 0.3.6.

Initialize Tversky instance.

Parameters
  • alpha (float) -- Tversky index parameter as described above

  • beta (float) -- Tversky index parameter as described above

  • bias (float) -- The symmetric Tversky index bias parameter

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Tversky index of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Tversky similarity

Return type

float

Raises

ValueError -- Unsupported weight assignment; alpha and beta must be greater than or equal to 0.

Examples

>>> cmp = Tversky()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.2222222222222222
>>> cmp.sim('aluminum', 'Catalan')
0.0625
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_tversky(src, tar, qval=2, alpha=1.0, beta=1.0, bias=None)[source]

Return the Tversky distance between two strings.

This is a wrapper for Tversky.dist().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alpha (float) -- Tversky index parameter as described above

  • beta (float) -- Tversky index parameter as described above

  • bias (float) -- The symmetric Tversky index bias parameter

Returns

Tversky distance

Return type

float

Examples

>>> dist_tversky('cat', 'hat')
0.6666666666666667
>>> dist_tversky('Niall', 'Neil')
0.7777777777777778
>>> dist_tversky('aluminum', 'Catalan')
0.9375
>>> dist_tversky('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Tversky.dist method instead.

abydos.distance.sim_tversky(src, tar, qval=2, alpha=1.0, beta=1.0, bias=None)[source]

Return the Tversky index of two strings.

This is a wrapper for Tversky.sim().

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • qval (int) -- The length of each q-gram

  • alpha (float) -- Tversky index parameter as described above

  • beta (float) -- Tversky index parameter as described above

  • bias (float) -- The symmetric Tversky index bias parameter

Returns

Tversky similarity

Return type

float

Examples

>>> sim_tversky('cat', 'hat')
0.3333333333333333
>>> sim_tversky('Niall', 'Neil')
0.2222222222222222
>>> sim_tversky('aluminum', 'Catalan')
0.0625
>>> sim_tversky('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Tversky.sim method instead.

class abydos.distance.UnigramSubtuple(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unigram subtuple similarity.

For two sets X and Y and a population N, unigram subtuple similarity [Pec10] is

\[sim_{unigram~subtuple}(X, Y) = log(\frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} {|X \setminus Y| \cdot |Y \setminus Y|}) - 3.29 \cdot \sqrt{\frac{1}{|X \cap Y|} + \frac{1}{|X \setminus Y|} + \frac{1}{|Y \setminus X|} + \frac{1}{|(N \setminus X) \setminus Y|}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{unigram~subtuple} = log(\frac{ad}{bc}) - 3.29 \cdot \sqrt{\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}}\]

New in version 0.4.0.

Initialize UnigramSubtuple instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the unigram subtuple similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unigram subtuple similarity

Return type

float

Examples

>>> cmp = UnigramSubtuple()
>>> cmp.sim('cat', 'hat')
0.6215275850074894
>>> cmp.sim('Niall', 'Neil')
0.39805896767519555
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the unigram subtuple similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unigram subtuple similarity

Return type

float

Examples

>>> cmp = UnigramSubtuple()
>>> cmp.sim_score('cat', 'hat')
1.9324426894059226
>>> cmp.sim_score('Niall', 'Neil')
1.4347242883606355
>>> cmp.sim_score('aluminum', 'Catalan')
-1.0866724701675263
>>> cmp.sim_score('ATCG', 'TAGC')
-0.461880260111438

New in version 0.4.0.

class abydos.distance.UnknownA(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown A correlation.

For two sets X and Y and a population N, Unknown A correlation is sometimes attributed to [Pei84]. It differs from Peirce in that the numerator is the product of the opposite pair of marginals:

\[corr_{UnknownA}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus Y|} {|Y| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{UnknownA} = \frac{ad-bc}{(a+c)(b+d)}\]

New in version 0.4.0.

Initialize UnknownA instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Unknown A correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown A correlation

Return type

float

Examples

>>> cmp = UnknownA()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.39486521181001283
>>> cmp.corr('aluminum', 'Catalan')
0.1147039897039897
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown A similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown A similarity

Return type

float

Examples

>>> cmp = UnknownA()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6974326059050064
>>> cmp.sim('aluminum', 'Catalan')
0.5573519948519948
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258

New in version 0.4.0.

class abydos.distance.UnknownB(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown B similarity.

For two sets X and Y and a population N, Unknown B similarity, which [Mor12] attributes to [Doo84] but could not be located in that source, is

\[sim_{UnknownB}(X, Y) = \frac{(|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)^2} {|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownB} = \frac{(ad-bc)^2}{(a+b)(a+c)(b+d)(c+d)}\]

New in version 0.4.0.

Initialize UnknownB instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown B similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown B similarity

Return type

float

Examples

>>> cmp = UnknownB()
>>> cmp.sim('cat', 'hat')
0.24744247205785666
>>> cmp.sim('Niall', 'Neil')
0.13009912077202224
>>> cmp.sim('aluminum', 'Catalan')
0.011710186806836291
>>> cmp.sim('ATCG', 'TAGC')
4.1196952743799446e-05

New in version 0.4.0.

class abydos.distance.UnknownC(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown C similarity.

For two sets X and Y and a population N, Unknown C similarity, which [Mor12] attributes to [Gow71] but could not be located in that source, is

\[sim_{UnknownC}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|} {\sqrt{|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownC} = \frac{a+d}{\sqrt{(a+b)(a+c)(b+d)(c+d)}}\]

New in version 0.4.0.

Initialize UnknownC instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown C similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown C similarity

Return type

float

Examples

>>> cmp = UnknownC()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.18222244271345164
>>> cmp.sim('aluminum', 'Catalan')
0.11686463498390019
>>> cmp.sim('ATCG', 'TAGC')
0.1987163029525032

New in version 0.4.0.

class abydos.distance.UnknownD(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown D similarity.

For two sets X and Y and a population N, Unknown D similarity, which [Mor12] attributes to [Pei84] but could not be located in that source, is

\[sim_{UnknownD}(X, Y) = \frac{|X \cap Y| \cdot |X \setminus Y| + |X \setminus Y| \cdot |Y \setminus X|} {|X \cap Y| \cdot |X \setminus Y| + 2 \cdot |X \setminus Y| \cdot |Y \setminus X| + |Y \setminus X| + |(N \setminus X) \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownD} = \frac{ab+bc}{ab+2bc+cd}\]

New in version 0.4.0.

Initialize UnknownD instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown D similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown D similarity

Return type

float

Examples

>>> cmp = UnknownD()
>>> cmp.sim('cat', 'hat')
0.00510204081632653
>>> cmp.sim('Niall', 'Neil')
0.00848536274925753
>>> cmp.sim('aluminum', 'Catalan')
0.011630019989096857
>>> cmp.sim('ATCG', 'TAGC')
0.006377551020408163

New in version 0.4.0.

class abydos.distance.UnknownE(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown E correlation.

For two sets X and Y and a population N, Unknown E correlation, which [Mor12] attributes to [GK54] but could not be located in that source, is

\[corr_{UnknownE}(X, Y) = \frac{2 \cdot min(|X \cap Y|, |(N \setminus X) \setminus Y|) - |X \setminus Y| - |Y \setminus X|} {2 \cdot min(|X \cap Y|, |(N \setminus X) \setminus Y|) + |X \setminus Y| + |Y \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{UnknownE} = \frac{2 \cdot min(a, d) - b - c}{2 \cdot min(a, d) + b + c}\]

New in version 0.4.0.

Initialize UnknownE instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Unknown E correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown E correlation

Return type

float

Examples

>>> cmp = UnknownE()
>>> cmp.corr('cat', 'hat')
0.0
>>> cmp.corr('Niall', 'Neil')
-0.2727272727272727
>>> cmp.corr('aluminum', 'Catalan')
-0.7647058823529411
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown E similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown E similarity

Return type

float

Examples

>>> cmp = UnknownE()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.11764705882352944
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.UnknownF(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown F similarity.

For two sets X and Y and a population N, Unknown F similarity, which [CCT10] attributes to [GW66] but could not be located in that source, is given as

\[sim(X, Y) = log(|X \cap Y|) - log(|N|) - log\Big(\frac{|X|}{|N|}\Big) - log\Big(\frac{|Y|}{|N|}\Big)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim = log(a) - log(n) - log\Big(\frac{a+b}{n}\Big) - log\Big(\frac{a+c}{n}\Big)\]

This formula is not very normalizable, so the following formula is used instead:

\[sim_{UnknownF}(X, Y) = min\Bigg(1, 1+log\Big(\frac{|X \cap Y|}{|N|}\Big) - \frac{1}{2}\Bigg(log\Big(\frac{|X|}{|N|}\Big) + log\Big(\frac{|Y|}{|N|}\Big)\Bigg)\Bigg)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownF} = min\Bigg(1, 1+log\Big(\frac{a}{n}\Big) - \frac{1}{2}\Bigg(log\Big(\frac{a+b}{n}\Big) + log\Big(\frac{a+c}{n}\Big)\Bigg)\Bigg)\]

New in version 0.4.0.

Initialize UnknownF instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Unknown F similarity

New in version 0.4.0.

sim(*args, **kwargs)[source]

Raise exception when called.

Parameters
  • *args -- Variable length argument list

  • **kwargs -- Arbitrary keyword arguments

Raises

NotImplementedError -- Method disabled for Unknown F similarity

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Unknown F similarity between two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown F similarity

Return type

float

Examples

>>> cmp = UnknownF()
>>> cmp.sim_score('cat', 'hat')
0.3068528194400555
>>> cmp.sim_score('Niall', 'Neil')
-0.007451510271132555
>>> cmp.sim_score('aluminum', 'Catalan')
-1.1383330595080272
>>> cmp.sim_score('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.UnknownG(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown G similarity.

For two sets X and Y and a population N, Unknown G similarity, which [CCT10] attributes to [Kulczynski27] but could not be located in that source, is

\[sim_{UnknownG}(X, Y) = \frac{\frac{|X \cap Y|}{2} \cdot (|X| + |Y|)} {|X| \cdot |Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownG} = \frac{\frac{a}{2} \cdot (2a+b+c)}{(a+b)(a+c)}\]

New in version 0.4.0.

Initialize UnknownG instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown G similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown G similarity

Return type

float

Examples

>>> cmp = UnknownG()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36666666666666664
>>> cmp.sim('aluminum', 'Catalan')
0.11805555555555555
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.UnknownH(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown H similarity.

For two sets X and Y and a population N, Unknown H similarity is a variant of Fager-McGowan index of affinity [Fag57][FM63]. It uses minimum rather than maximum in the denominator of the second term, and is sometimes misidentified as the Fager-McGown index of affinity (cf. [Whi82], for example).

\[sim_{UnknownH}(X, Y) = \frac{|X \cap Y|}{\sqrt{|X|\cdot|Y|}} - \frac{1}{2\sqrt{min(|X|, |Y|)}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownH} = \frac{a}{\sqrt{(a+b)(a+c)}} - \frac{1}{2\sqrt{min(a+b, a+c)}}\]

New in version 0.4.0.

Initialize UnknownH instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Unknown H similarity of two strings.

As this similarity ranges from \((-\inf, 1.0)\), this normalization simply clamps the value to the range (0.0, 1.0).

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Unknown H similarity

Return type

float

Examples

>>> cmp = UnknownH()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.14154157392013175
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Unknown H similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown H similarity

Return type

float

Examples

>>> cmp = UnknownH()
>>> cmp.sim('cat', 'hat')
0.25
>>> cmp.sim('Niall', 'Neil')
0.14154157392013175
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.UnknownI(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown I similarity.

For two sets X and Y, the Unknown I similarity is based on Mountford similarity [Mou62] Mountford.

\[sim_{UnknownI}(X, Y) = \frac{2(|X \cap Y|+1)}{2((|X|+2)\cdot(|Y|+2))- (|X|+|Y|+4)\cdot(|X \cap Y|+1)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownI} = \frac{2(a+1)}{2(a+b+2)(a+c+2)-(2a+b+c+4)(a+1)}\]

New in version 0.4.0.

Initialize UnknownI instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown I similarity

Return type

float

Examples

>>> cmp = UnknownI()
>>> cmp.sim('cat', 'hat')
0.16666666666666666
>>> cmp.sim('Niall', 'Neil')
0.08955223880597014
>>> cmp.sim('aluminum', 'Catalan')
0.02247191011235955
>>> cmp.sim('ATCG', 'TAGC')
0.023809523809523808

New in version 0.4.0.

class abydos.distance.UnknownJ(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown J similarity.

For two sets X and Y and a population N, Unknown J similarity, which [Seq18] attributes to "Kocher & Wang" but could not be located, is

\[sim_{UnknownJ}(X, Y) = |X \cap Y| \cdot \frac{|N|}{|X| \cdot |N \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownJ} = a \cdot \frac{n}{(a+b)(c+d)}\]

New in version 0.4.0.

Initialize UnknownJ instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Unknown J similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Unknown J similarity

Return type

float

Examples

>>> cmp = UnknownJ()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.33333333333333337
>>> cmp.sim('aluminum', 'Catalan')
0.11111111111111112
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Unknown J similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown J similarity

Return type

float

Examples

>>> cmp = UnknownJ()
>>> cmp.sim_score('cat', 'hat')
0.5025641025641026
>>> cmp.sim_score('Niall', 'Neil')
0.33590402742073694
>>> cmp.sim_score('aluminum', 'Catalan')
0.11239977090492555
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.UnknownK(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown K distance.

For two sets X and Y and a population N, Unknown K distance, which [Seq18] attributes to "Excoffier" but could not be located, is

\[dist_{UnknownK}(X, Y) = |N| \cdot (1 - \frac{|X \cap Y|}{|N|})\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{UnknownK} = n \cdot (1 - \frac{a}{n})\]

New in version 0.4.0.

Initialize UnknownK instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Unknown K distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Unknown K distance

Return type

float

Examples

>>> cmp = UnknownK()
>>> cmp.dist('cat', 'hat')
0.9974489795918368
>>> cmp.dist('Niall', 'Neil')
0.9974489795918368
>>> cmp.dist('aluminum', 'Catalan')
0.9987261146496815
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Unknown K distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown K distance

Return type

float

Examples

>>> cmp = UnknownK()
>>> cmp.dist_abs('cat', 'hat')
782.0
>>> cmp.dist_abs('Niall', 'Neil')
782.0
>>> cmp.dist_abs('aluminum', 'Catalan')
784.0
>>> cmp.dist_abs('ATCG', 'TAGC')
784.0

New in version 0.4.0.

class abydos.distance.UnknownL(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown L similarity.

For two sets X and Y and a population N, Unknown L similarity, which [Seq18] attributes to "Roux" but could not be located, is

\[sim_{UnknownL}(X, Y) = \frac{|X \cap Y| + |(N \setminus X) \setminus Y|} {min(|X \setminus Y|, |Y \setminus X|) + min(|N|-|X \setminus Y|, |N|-|Y \setminus X|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownL} = \frac{a+d}{min(b, c) + min(n-b, n-c)}\]

New in version 0.4.0.

Initialize UnknownL instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Unknown L similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown L similarity

Return type

float

Examples

>>> cmp = UnknownL()
>>> cmp.sim('cat', 'hat')
0.9948979591836735
>>> cmp.sim('Niall', 'Neil')
0.9923371647509579
>>> cmp.sim('aluminum', 'Catalan')
0.9821428571428571
>>> cmp.sim('ATCG', 'TAGC')
0.9872448979591837

New in version 0.4.0.

class abydos.distance.UnknownM(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Unknown M similarity.

For two sets X and Y and a population N, Unknown < similarity, which [Seq18] attributes to "Roux" but could not be located, is

\[sim_{UnknownM}(X, Y) = \frac{|N|-|X \cap Y| \cdot |(N \setminus X) \setminus Y|} {\sqrt{|X| \cdot |N \setminus X| \cdot |Y| \cdot |N \setminus Y|}}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{UnknownM} = \frac{n-ad}{\sqrt{(a+b)(c+d)(a+c)(b+d)}}\]

New in version 0.4.0.

Initialize UnknownM instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Unknown M similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Unknown M similarity

Return type

float

Examples

>>> cmp = UnknownM()
>>> cmp.sim('cat', 'hat')
0.6237179487179487
>>> cmp.sim('Niall', 'Neil')
0.5898213585061158
>>> cmp.sim('aluminum', 'Catalan')
0.49878582197419324
>>> cmp.sim('ATCG', 'TAGC')
0.3993581514762516

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Unknown M similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Unknown M similarity

Return type

float

Examples

>>> cmp = UnknownM()
>>> cmp.sim_score('cat', 'hat')
-0.24743589743589745
>>> cmp.sim_score('Niall', 'Neil')
-0.17964271701223158
>>> cmp.sim_score('aluminum', 'Catalan')
0.0024283560516135103
>>> cmp.sim_score('ATCG', 'TAGC')
0.2012836970474968

New in version 0.4.0.

class abydos.distance.Upholt(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Upholt similarity.

For two sets X and Y and a population N, Upholt similarity, Upholt's S, [Uph77] is

\[sim_{Upholt}(X, Y) = \frac{1}{2}\Bigg(-\frac{2 \cdot |X \cap Y|}{|X| + |Y|} + \sqrt{\Big(\frac{2 \cdot |X \cap Y|}{|X| + |Y|}\Big)^2 + 8\frac{2 \cdot |X \cap Y|}{|X| + |Y|}}\Bigg)\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Upholt}(X, Y) = \frac{1}{2}\Bigg(-\frac{2a}{2a+b+c} + \sqrt{\Big(\frac{2a}{2a+b+c}\Big)^2 + 8\frac{2a}{2a+b+c}}\Bigg)\]

New in version 0.4.0.

Initialize Upholt instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Upholt similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Upholt similarity

Return type

float

Examples

>>> cmp = Upholt()
>>> cmp.sim('cat', 'hat')
0.7807764064044151
>>> cmp.sim('Niall', 'Neil')
0.6901511860568581
>>> cmp.sim('aluminum', 'Catalan')
0.42980140370106323
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.WarrensI(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Warrens I correlation.

For two sets X and Y, Warrens I correlation \(S_{NS1}\) [War08] is

\[corr_{WarrensI}(X, Y) = \frac{2|X \cap Y| - |X \setminus Y| - |Y \setminus X|} {2|X \cap Y| + |X \setminus Y| + |Y \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{WarrensI} = \frac{2a-b-c}{2a+b+c}\]

New in version 0.4.0.

Initialize WarrensI instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Warrens I correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens I correlation

Return type

float

Examples

>>> cmp = WarrensI()
>>> cmp.corr('cat', 'hat')
0.0
>>> cmp.corr('Niall', 'Neil')
-0.2727272727272727
>>> cmp.corr('aluminum', 'Catalan')
-0.7647058823529411
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return the Warrens I similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens I similarity

Return type

float

Examples

>>> cmp = WarrensI()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.11764705882352944
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.WarrensII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Warrens II similarity.

For two sets X and Y and a population N, Warrens II similarity \(S_{NS2}\) [War08] is

\[sim_{WarrensII}(X, Y) = \frac{2|(N \setminus X) \setminus Y|} {|N \setminus X| + |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{WarrensII} = \frac{2d}{b+c+2d}\]

New in version 0.4.0.

Initialize WarrensII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Warrens II similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens II similarity

Return type

float

Examples

>>> cmp = WarrensII()
>>> cmp.sim('cat', 'hat')
0.9974358974358974
>>> cmp.sim('Niall', 'Neil')
0.9955041746949261
>>> cmp.sim('aluminum', 'Catalan')
0.9903412749517064
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516

New in version 0.4.0.

class abydos.distance.WarrensIII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Warrens III correlation.

For two sets X and Y and a population N, Warrens III correlation \(S_{NS3}\) [War08] is

\[corr_{WarrensIII}(X, Y) = \frac{2|(N \setminus X) \setminus Y| - |X \setminus Y| - |Y \setminus X|}{|N \setminus X| + |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{WarrensIII} = \frac{2d-b-c}{2d+b+c}\]

New in version 0.4.0.

Initialize WarrensIII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return the Warrens III correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens III correlation

Return type

float

Examples

>>> cmp = WarrensIII()
>>> cmp.corr('cat', 'hat')
0.9948717948717949
>>> cmp.corr('Niall', 'Neil')
0.9910083493898523
>>> cmp.corr('aluminum', 'Catalan')
0.9806825499034127
>>> cmp.corr('ATCG', 'TAGC')
0.9871630295250321

New in version 0.4.0.

sim(src, tar)[source]

Return the Warrens III similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens III similarity

Return type

float

Examples

>>> cmp = WarrensIII()
>>> cmp.sim('cat', 'hat')
0.9974358974358974
>>> cmp.sim('Niall', 'Neil')
0.9955041746949261
>>> cmp.sim('aluminum', 'Catalan')
0.9903412749517064
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516

New in version 0.4.0.

class abydos.distance.WarrensIV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Warrens IV similarity.

For two sets X and Y and a population N, Warrens IV similarity [War08] is

\[sim_{WarrensIV}(X, Y) = \frac{4|X \cap Y| \cdot |(N \setminus X) \setminus Y|} {4|X \cap Y| \cdot |(N \setminus X) \setminus Y| + (|X \cap Y| + |(N \setminus X) \setminus Y|) (|X \setminus Y| + |Y \setminus X|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{WarrensIV} = \frac{4ad}{4ad + (a+d)(b+c)}\]

New in version 0.4.0.

Initialize WarrensIV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Warrens IV similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens IV similarity

Return type

float

Examples

>>> cmp = WarrensIV()
>>> cmp.sim('cat', 'hat')
0.666095890410959
>>> cmp.sim('Niall', 'Neil')
0.5326918120113412
>>> cmp.sim('aluminum', 'Catalan')
0.21031040612607685
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.WarrensV(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Warrens V similarity.

For two sets X and Y and a population N, Warrens V similarity [War08] is

\[sim_{WarrensV}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {min(|X| \cdot |Y|, |N \setminus X| \cdot |N \setminus Y|)}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{WarrensV} = \frac{ad-bc}{min( (a+b)(a+c), (b+d)(c+d) )}\]

New in version 0.4.0.

Initialize WarrensV instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Warrens V similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Warrens V similarity

Return type

float

Examples

>>> cmp = WarrensV()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3333333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.11125283446712018
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Warrens V similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Warrens V similarity

Return type

float

Examples

>>> cmp = WarrensV()
>>> cmp.sim_score('cat', 'hat')
97.0
>>> cmp.sim_score('Niall', 'Neil')
51.266666666666666
>>> cmp.sim_score('aluminum', 'Catalan')
9.902777777777779
>>> cmp.sim_score('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

class abydos.distance.WeightedJaccard(tokenizer=None, intersection_type='crisp', weight=3, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Weighted Jaccard similarity.

For two sets X and Y and a weight w, the Weighted Jaccard similarity [LL98] is

\[sim_{Jaccard_w}(X, Y) = \frac{w \cdot |X \cap Y|} {w \cdot |X \cap Y| + |X \setminus Y| + |Y \setminus X|}\]

Here, the intersection between the two sets is weighted by w. Compare to Jaccard similarity (\(w = 1\)), and to Dice similarity (\(w = 2\)). In the default case, the weight of the intersection is 3, following [LL98].

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Jaccard_w} = \frac{w\cdot a}{w\cdot a+b+c}\]

New in version 0.4.0.

Initialize TripleWeightedJaccard instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • weight (int) -- The weight to apply to the intersection cardinality. (3, by default.)

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the Triple Weighted Jaccard similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Weighted Jaccard similarity

Return type

float

Examples

>>> cmp = WeightedJaccard()
>>> cmp.sim('cat', 'hat')
0.6
>>> cmp.sim('Niall', 'Neil')
0.46153846153846156
>>> cmp.sim('aluminum', 'Catalan')
0.16666666666666666
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Whittaker(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Whittaker distance.

For two multisets X and Y drawn from an alphabet S, Whittaker distance [Whi52] is

\[sim_{Whittaker}(X, Y) = 1 - \frac{1}{2}\sum_{i \in S} \Bigg| \frac{|X_i|}{|X|} - \frac{|Y_i|}{|Y|} \Bigg|\]

New in version 0.4.0.

Initialize Whittaker instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Whittaker distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Whittaker distance

Return type

float

Examples

>>> cmp = Whittaker()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.33333333333333
>>> cmp.sim('aluminum', 'Catalan')
0.11111111111111
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.YatesChiSquared(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Yates's Chi-Squared similarity.

For two sets X and Y and a population N, Yates's \(\chi^2\) similarity [Yat34] is

\[sim_{Yates_{\chi^2}}(X, Y) = \frac{|N| \cdot (||X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|| - \frac{|N|}{2})^2} {|X| \cdot |N \setminus X| \cdot |Y| \cdot |N \setminus Y|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[sim_{Yates_{\chi^2}} = \frac{n \cdot (|ad-bc| - \frac{n}{2})^2}{(a+b)(c+d)(a+c)(b+d)}\]

New in version 0.4.0.

Initialize YatesChiSquared instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return Yates's normalized Chi-Squared similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Yates's Chi-Squared similarity

Return type

float

Examples

>>> cmp = YatesChiSquared()
>>> cmp.sim('cat', 'hat')
0.18081199852082455
>>> cmp.sim('Niall', 'Neil')
0.08608296705052738
>>> cmp.sim('aluminum', 'Catalan')
0.0026563223707532654
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar, signed=False)[source]

Return Yates's Chi-Squared similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

  • signed (bool) -- If True, negative correlations will carry a negative sign

Returns

Yates's Chi-Squared similarity

Return type

float

Examples

>>> cmp = YatesChiSquared()
>>> cmp.sim_score('cat', 'hat')
108.37343852728468
>>> cmp.sim_score('Niall', 'Neil')
56.630055670871954
>>> cmp.sim_score('aluminum', 'Catalan')
1.8574215841854373
>>> cmp.sim_score('ATCG', 'TAGC')
6.960385076156687

New in version 0.4.0.

class abydos.distance.YuleQ(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Yule's Q correlation.

For two sets X and Y and a population N, Yule's Q correlation [Yul12] is

\[corr_{Yule_Q}(X, Y) = \frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|} {|X \cap Y| \cdot |(N \setminus X) \setminus Y| + |X \setminus Y| \cdot |Y \setminus X|}\]

Yule himself terms this the coefficient of association.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Yule_Q} = \frac{ad-bc}{ad+bc}\]

New in version 0.4.0.

Initialize YuleQ instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return Yule's Q correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Yule's Q correlation

Return type

float

Examples

>>> cmp = YuleQ()
>>> cmp.corr('cat', 'hat')
0.9948717948717949
>>> cmp.corr('Niall', 'Neil')
0.9846350832266325
>>> cmp.corr('aluminum', 'Catalan')
0.8642424242424243
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return Yule's Q similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Yule's Q similarity

Return type

float

Examples

>>> cmp = YuleQ()
>>> cmp.sim('cat', 'hat')
0.9974358974358974
>>> cmp.sim('Niall', 'Neil')
0.9923175416133163
>>> cmp.sim('aluminum', 'Catalan')
0.9321212121212121
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.YuleQII(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Yule's Q dissimilarity.

For two sets X and Y and a population N, Yule's Q dissimilarity [YK68] is

\[dist_{Yule_QII}(X, Y) = \frac{2 \cdot |X \setminus Y| \cdot |Y \setminus X|} {|X \cap Y| \cdot |(N \setminus X) \setminus Y| + |X \setminus Y| \cdot |Y \setminus X|}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{Yule_QII} = \frac{2bc}{ad+bc}\]

New in version 0.4.0.

Initialize YuleQII instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return normalized Yule's Q dissimilarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Yule's Q II distance

Return type

float

Examples

>>> cmp = YuleQII()
>>> cmp.dist('cat', 'hat')
0.002564102564102564
>>> cmp.dist('Niall', 'Neil')
0.0076824583866837385
>>> cmp.dist('aluminum', 'Catalan')
0.06787878787878789
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return Yule's Q dissimilarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Yule's Q II distance

Return type

float

Examples

>>> cmp = YuleQII()
>>> cmp.dist_abs('cat', 'hat')
0.005128205128205128
>>> cmp.dist_abs('Niall', 'Neil')
0.015364916773367477
>>> cmp.dist_abs('aluminum', 'Catalan')
0.13575757575757577
>>> cmp.dist_abs('ATCG', 'TAGC')
2.0

New in version 0.4.0.

class abydos.distance.YuleY(alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Yule's Y correlation.

For two sets X and Y and a population N, Yule's Y correlation [Yul12] is

\[corr_{Yule_Y}(X, Y) = \frac{\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} - \sqrt{|X \setminus Y| \cdot |Y \setminus X|}} {\sqrt{|X \cap Y| \cdot |(N \setminus X) \setminus Y|} + \sqrt{|X \setminus Y| \cdot |Y \setminus X|}}\]

In [Yul12], this is labeled \(\omega\), so it is sometimes referred to as Yule's \(\omega\). Yule himself terms this the coefficient of colligation.

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[corr_{Yule_Y} = \frac{\sqrt{ad}-\sqrt{bc}}{\sqrt{ad}+\sqrt{bc}}\]

New in version 0.4.0.

Initialize YuleY instance.

Parameters
  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

corr(src, tar)[source]

Return Yule's Y correlation of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Yule's Y correlation

Return type

float

Examples

>>> cmp = YuleY()
>>> cmp.corr('cat', 'hat')
0.9034892632818762
>>> cmp.corr('Niall', 'Neil')
0.8382551144735259
>>> cmp.corr('aluminum', 'Catalan')
0.5749826820237787
>>> cmp.corr('ATCG', 'TAGC')
-1.0

New in version 0.4.0.

sim(src, tar)[source]

Return Yule's Y similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Yule's Y similarity

Return type

float

Examples

>>> cmp = YuleY()
>>> cmp.sim('cat', 'hat')
0.9517446316409381
>>> cmp.sim('Niall', 'Neil')
0.919127557236763
>>> cmp.sim('aluminum', 'Catalan')
0.7874913410118893
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.YJHHR(pval=1, alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

YJHHR distance.

For two sets X and Y and a parameter p, YJHHR distance [YJH+16] is

\[dist_{YJHHR_p}(X, Y) = \sqrt[p]{|X \setminus Y|^p + |Y \setminus X|^p}\]

In 2x2 confusion table terms, where a+b+c+d=n, this is

\[dist_{YJHHR} = \sqrt[p]{b^p + c^p}\]

New in version 0.4.0.

Initialize YJHHR instance.

Parameters
  • pval (int) -- The \(p\)-value of the \(L^p\)-space

  • alphabet (Counter, collection, int, or None) -- This represents the alphabet of possible tokens. See alphabet description in _TokenDistance for details.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized YJHHR distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

normalized YJHHR distance

Return type

float

Examples

>>> cmp = YJHHR()
>>> cmp.dist('cat', 'hat')
0.6666666666666666
>>> cmp.dist('Niall', 'Neil')
0.7777777777777778
>>> cmp.dist('aluminum', 'Catalan')
0.9375
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the YJHHR distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

YJHHR distance

Return type

float

Examples

>>> cmp = YJHHR()
>>> cmp.dist_abs('cat', 'hat')
4.0
>>> cmp.dist_abs('Niall', 'Neil')
7.0
>>> cmp.dist_abs('aluminum', 'Catalan')
15.0
>>> cmp.dist_abs('ATCG', 'TAGC')
10.0

New in version 0.4.0.

class abydos.distance.Bhattacharyya(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Bhattacharyya distance.

For two multisets X and Y drawn from an alphabet S, Bhattacharyya distance [Bha46] is

\[dist_{Bhattacharyya}(X, Y) = -log(\sum_{i \in S} \sqrt{X_iY_i})\]

New in version 0.4.0.

Initialize Bhattacharyya instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the Bhattacharyya coefficient of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Bhattacharyya distance

Return type

float

Examples

>>> cmp = Bhattacharyya()
>>> cmp.dist('cat', 'hat')
0.5
>>> cmp.dist('Niall', 'Neil')
0.3651483716701107
>>> cmp.dist('aluminum', 'Catalan')
0.11785113019775792
>>> cmp.dist('ATCG', 'TAGC')
0.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Bhattacharyya distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Bhattacharyya distance

Return type

float

Examples

>>> cmp = Bhattacharyya()
>>> cmp.dist_abs('cat', 'hat')
0.6931471805599453
>>> cmp.dist_abs('Niall', 'Neil')
1.0074515102711326
>>> cmp.dist_abs('aluminum', 'Catalan')
2.1383330595080277
>>> cmp.dist_abs('ATCG', 'TAGC')
-inf

New in version 0.4.0.

class abydos.distance.BrainerdRobinson(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Brainerd-Robinson similarity.

For two multisets X and Y drawn from an alphabet S, Brainerd-Robinson similarity [Rob51][Bra51] is

\[sim_{BrainerdRobinson}(X, Y) = 200 - 100 \cdot \sum_{i \in S} |\frac{X_i}{\sum_{i \in S} |X_i|} - \frac{Y_i}{\sum_{i \in S} |Y_i|}|\]

New in version 0.4.0.

Initialize BrainerdRobinson instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Brainerd-Robinson similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Brainerd-Robinson similarity

Return type

float

Examples

>>> cmp = BrainerdRobinson()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3333333333333334
>>> cmp.sim('aluminum', 'Catalan')
0.111111111111111
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Brainerd-Robinson similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Brainerd-Robinson similarity

Return type

float

Examples

>>> cmp = BrainerdRobinson()
>>> cmp.sim_score('cat', 'hat')
100.0
>>> cmp.sim_score('Niall', 'Neil')
66.66666666666669
>>> cmp.sim_score('aluminum', 'Catalan')
22.2222222222222
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.QuantitativeCosine(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Quantitative Cosine similarity.

For two multisets X and Y drawn from an alphabet S, Quantitative Cosine similarity is

\[sim_{QuantitativeCosine}(X, Y) = \frac{\sum_{i \in S} X_iY_i} {\sqrt{\sum_{i \in S} X_i^2}\sqrt{\sum_{i \in S} Y_i^2}}\]

New in version 0.4.0.

Initialize QuantitativeCosine instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Quantitative Cosine similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Quantitative Cosine similarity

Return type

float

Examples

>>> cmp = QuantitativeCosine()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3651483716701107
>>> cmp.sim('aluminum', 'Catalan')
0.10660035817780521
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.QuantitativeDice(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Quantitative Dice similarity.

For two multisets X and Y drawn from an alphabet S, Quantitative Dice similarity is

\[sim_{QuantitativeDice}(X, Y) = \frac{2 \cdot \sum_{i \in S} X_iY_i} {\sum_{i \in S} X_i^2 + \sum_{i \in S} Y_i^2}\]

New in version 0.4.0.

Initialize QuantitativeDice instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Quantitative Dice similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Quantitative Dice similarity

Return type

float

Examples

>>> cmp = QuantitativeDice()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.10526315789473684
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.QuantitativeJaccard(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Quantitative Jaccard similarity.

For two multisets X and Y drawn from an alphabet S, Quantitative Jaccard similarity is

\[sim_{QuantitativeJaccard}(X, Y) = \frac{\sum_{i \in S} X_iY_i} {\sum_{i \in S} X_i^2 + \sum_{i \in S} Y_i^2 - \sum_{i \in S} X_iY_i}\]

New in version 0.4.0.

Initialize QuantitativeJaccard instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Quantitative Jaccard similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Quantitative Jaccard similarity

Return type

float

Examples

>>> cmp = QuantitativeJaccard()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.2222222222222222
>>> cmp.sim('aluminum', 'Catalan')
0.05555555555555555
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.Roberts(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Roberts similarity.

For two multisets X and Y drawn from an alphabet S, Roberts similarity [Rob86] is

\[sim_{Roberts}(X, Y) = \frac{\Big[\sum_{i \in S} (X_i + Y_i) \cdot \frac{min(X_i, Y_i)}{max(X_i, Y_i)}\Big]} {\sum_{i \in S} (X_i + Y_i)}\]

New in version 0.4.0.

Initialize Roberts instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Roberts similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Roberts similarity

Return type

float

Examples

>>> cmp = Roberts()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.11764705882352941
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.AverageLinkage(tokenizer=None, metric=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Average linkage distance.

For two lists of tokens X and Y, average linkage distance [DD16] is

\[dist_{AverageLinkage}(X, Y) = \frac{\sum_{i \in X} \sum_{j \in Y} dist(X_i, Y_j)}{|X| \cdot |Y|}\]

New in version 0.4.0.

Initialize AverageLinkage instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants. (Defaults to Levenshtein distance)

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the average linkage distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

average linkage distance

Return type

float

Examples

>>> cmp = AverageLinkage()
>>> cmp.dist('cat', 'hat')
0.8125
>>> cmp.dist('Niall', 'Neil')
0.8333333333333334
>>> cmp.dist('aluminum', 'Catalan')
0.9166666666666666
>>> cmp.dist('ATCG', 'TAGC')
0.8

New in version 0.4.0.

class abydos.distance.SingleLinkage(tokenizer=None, metric=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Single linkage distance.

For two multisets X and Y, single linkage distance [DD16] is

\[dist_{SingleLinkage}(X, Y) = min_{i \in X, j \in Y} dist(X_i, Y_j)\]

New in version 0.4.0.

Initialize SingleLinkage instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants. (Defaults to Levenshtein distance)

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized single linkage distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

normalized single linkage distance

Return type

float

Examples

>>> cmp = SingleLinkage()
>>> cmp.dist('cat', 'hat')
0.0
>>> cmp.dist('Niall', 'Neil')
0.0
>>> cmp.dist('aluminum', 'Catalan')
0.0
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the single linkage distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

single linkage distance

Return type

float

Examples

>>> cmp = SingleLinkage()
>>> cmp.dist_abs('cat', 'hat')
0.0
>>> cmp.dist_abs('Niall', 'Neil')
0.0
>>> cmp.dist_abs('aluminum', 'Catalan')
0.0
>>> cmp.dist_abs('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.CompleteLinkage(tokenizer=None, metric=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Complete linkage distance.

For two multisets X and Y, complete linkage distance [DD16] is

\[sim_{CompleteLinkage}(X, Y) = max_{i \in X, j \in Y} dist(X_i, Y_j)\]

New in version 0.4.0.

Initialize CompleteLinkage instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants. (Defaults to Levenshtein distance)

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized complete linkage distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

normalized complete linkage distance

Return type

float

Examples

>>> cmp = CompleteLinkage()
>>> cmp.dist('cat', 'hat')
1.0
>>> cmp.dist('Niall', 'Neil')
1.0
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the complete linkage distance of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

complete linkage distance

Return type

float

Examples

>>> cmp = CompleteLinkage()
>>> cmp.dist_abs('cat', 'hat')
2
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('aluminum', 'Catalan')
2
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.4.0.

class abydos.distance.Bag(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Bag distance.

Bag distance is proposed in [BCP02]. It is defined as

\[dist_{bag}(src, tar) = max(|multiset(src)-multiset(tar)|, |multiset(tar)-multiset(src)|)\]

New in version 0.3.6.

Initialize Bag instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized bag distance between two strings.

Bag distance is normalized by dividing by \(max( |src|, |tar| )\).

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized bag distance

Return type

float

Examples

>>> cmp = Bag()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.4
>>> cmp.dist('aluminum', 'Catalan')
0.625
>>> cmp.dist('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar, normalized=False)[source]

Return the bag distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • normalized (bool) -- Normalizes to [0, 1] if True

Returns

Bag distance

Return type

int or float

Examples

>>> cmp = Bag()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('aluminum', 'Catalan')
5
>>> cmp.dist_abs('ATCG', 'TAGC')
0
>>> cmp.dist_abs('abcdefg', 'hijklm')
7
>>> cmp.dist_abs('abcdefg', 'hijklmno')
8

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.bag(src, tar)[source]

Return the bag distance between two strings.

This is a wrapper for Bag.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Bag distance

Return type

int

Examples

>>> bag('cat', 'hat')
1
>>> bag('Niall', 'Neil')
2
>>> bag('aluminum', 'Catalan')
5
>>> bag('ATCG', 'TAGC')
0
>>> bag('abcdefg', 'hijklm')
7
>>> bag('abcdefg', 'hijklmno')
8

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Bag.dist_abs method instead.

abydos.distance.dist_bag(src, tar)[source]

Return the normalized bag distance between two strings.

This is a wrapper for Bag.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized bag distance

Return type

float

Examples

>>> dist_bag('cat', 'hat')
0.3333333333333333
>>> dist_bag('Niall', 'Neil')
0.4
>>> dist_bag('aluminum', 'Catalan')
0.625
>>> dist_bag('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Bag.dist method instead.

abydos.distance.sim_bag(src, tar)[source]

Return the normalized bag similarity of two strings.

This is a wrapper for Bag.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized bag similarity

Return type

float

Examples

>>> round(sim_bag('cat', 'hat'), 12)
0.666666666667
>>> sim_bag('Niall', 'Neil')
0.6
>>> sim_bag('aluminum', 'Catalan')
0.375
>>> sim_bag('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Bag.sim method instead.

class abydos.distance.SoftCosine(tokenizer=None, metric=None, sim_method='a', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Soft Cosine similarity.

As described in [SGGomezAP14], soft cosine similarity of two multi-sets X and Y, drawn from an alphabet S, is

\[sim_{soft cosine}(X, Y) = \frac{\sum_{i \in S}\sum_{j \in S} s_{ij} X_i Y_j} {\sqrt{\sum_{i \in S}\sum_{j \in S} s_{ij} X_i X_j} \sqrt{\sum_{i \in S}\sum_{j \in S} s_{ij} Y_i Y_j}}\]

where \(s_{ij}\) is the similarity of two tokens, by default a function of Levenshtein distance: \(\frac{1}{1+Levenshtein\_distance(i, j)}\).

Notes

This class implements soft cosine similarity, as defined by [SGGomezAP14]. An alternative formulation of soft cosine similarity using soft (multi-)sets is provided by the Cosine class using intersection_type=``soft``, based on the soft intersection defined in [RHJF14].

New in version 0.4.0.

Initialize SoftCosine instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package, defaulting to the QGrams tokenizer with q=4

  • threshold (float) -- The minimum similarity for a pair of tokens to contribute to similarity

  • metric (_Distance) -- A distance instance from the abydos.distance package, defaulting to Levenshtein distance

  • sim_method (str) --

    Selects the similarity method from the four given in [SGGomezAP14]:

    • a : \(\frac{1}{1+d}\)

    • b : \(1-\frac{d}{m}\)

    • c : \(\sqrt{1-\frac{d}{m}}\)

    • d : \(\Big(1-\frac{d}{m}\Big)^2\)

    Where \(d\) is the distance (Levenshtein by default) and \(m\) is the maximum length of the two tokens. Option a is default, as suggested by the paper.

  • **kwargs -- Arbitrary keyword arguments

Raises

ValueError -- sim_method must be one of 'a', 'b', 'c', or 'd'

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Soft Cosine similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fuzzy Cosine similarity

Return type

float

Examples

>>> cmp = SoftCosine()
>>> cmp.sim('cat', 'hat')
0.8750000000000001
>>> cmp.sim('Niall', 'Neil')
0.8844691709074513
>>> cmp.sim('aluminum', 'Catalan')
0.831348688760277
>>> cmp.sim('ATCG', 'TAGC')
0.8571428571428572

New in version 0.4.0.

class abydos.distance.MongeElkan(sim_func=None, symmetric=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Monge-Elkan similarity.

Monge-Elkan is defined in [ME96].

Note: Monge-Elkan is NOT a symmetric similarity algorithm. Thus, the similarity of src to tar is not necessarily equal to the similarity of tar to src. If the symmetric argument is True, a symmetric value is calculated, at the cost of doubling the computation time (since \(sim_{Monge-Elkan}(src, tar)\) and \(sim_{Monge-Elkan}(tar, src)\) are both calculated and then averaged).

New in version 0.3.6.

Initialize MongeElkan instance.

Parameters
  • sim_func (function) -- The internal similarity metric to employ

  • symmetric (bool) -- Return a symmetric similarity measure

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the Monge-Elkan similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Monge-Elkan similarity

Return type

float

Examples

>>> cmp = MongeElkan()
>>> cmp.sim('cat', 'hat')
0.75
>>> round(cmp.sim('Niall', 'Neil'), 12)
0.666666666667
>>> round(cmp.sim('aluminum', 'Catalan'), 12)
0.388888888889
>>> cmp.sim('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_monge_elkan(src, tar, sim_func=<function sim_levenshtein>, symmetric=False)[source]

Return the Monge-Elkan distance between two strings.

This is a wrapper for MongeElkan.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • sim_func (function) -- The internal similarity metric to employ

  • symmetric (bool) -- Return a symmetric similarity measure

Returns

Monge-Elkan distance

Return type

float

Examples

>>> dist_monge_elkan('cat', 'hat')
0.25
>>> round(dist_monge_elkan('Niall', 'Neil'), 12)
0.333333333333
>>> round(dist_monge_elkan('aluminum', 'Catalan'), 12)
0.611111111111
>>> dist_monge_elkan('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MongeElkan.dist method instead.

abydos.distance.sim_monge_elkan(src, tar, sim_func=<function sim_levenshtein>, symmetric=False)[source]

Return the Monge-Elkan similarity of two strings.

This is a wrapper for MongeElkan.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • sim_func (function) -- Rhe internal similarity metric to employ

  • symmetric (bool) -- Return a symmetric similarity measure

Returns

Monge-Elkan similarity

Return type

float

Examples

>>> sim_monge_elkan('cat', 'hat')
0.75
>>> round(sim_monge_elkan('Niall', 'Neil'), 12)
0.666666666667
>>> round(sim_monge_elkan('aluminum', 'Catalan'), 12)
0.388888888889
>>> sim_monge_elkan('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MongeElkan.sim method instead.

class abydos.distance.TFIDF(tokenizer=None, corpus=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

TF-IDF similarity.

For two sets X and Y and a population N, TF-IDF similarity [CRF03] is

\[ \begin{align}\begin{aligned}sim_{TF-IDF}(X, Y) = \sum_{w \in X \cap Y} V(w, X) \cdot V(w, Y)\\V(w, S) = \frac{V'(w, S)}{\sqrt{\sum_{w \in S} V'(w, S)^2}}\\V'(w, S) = log(1+TF_{w,S}) \cdot log(1+IDF_w)\end{aligned}\end{align} \]

Notes

One is added to both the TF & IDF values before taking the logarithm to ensure the logarithms do not fall to 0, which will tend to result in 0.0 similarities even when there is a degree of matching.

New in version 0.4.0.

Initialize TFIDF instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • corpus (UnigramCorpus) -- A unigram corpus UnigramCorpus. If None, a corpus will be created from the two words when a similarity function is called.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the TF-IDF similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

TF-IDF similarity

Return type

float

Examples

>>> cmp = TFIDF()
>>> cmp.sim('cat', 'hat')
0.30404449697373
>>> cmp.sim('Niall', 'Neil')
0.20108911303601
>>> cmp.sim('aluminum', 'Catalan')
0.05355175631194
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.SoftTFIDF(tokenizer=None, corpus=None, metric=None, threshold=0.9, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

SoftTF-IDF similarity.

For two sets X and Y and a population N, SoftTF-IDF similarity [CRF03] is

\[\begin{split}\begin{array}{ll} sim_{SoftTF-IDF}(X, Y) &= \sum_{w \in \{sim_{metric}(x, y) \ge \theta | x \in X, y \in Y \}} V(w, S) \cdot V(w, X) \cdot V(w, Y) \\ \\ V(w, S) &= \frac{V'(w, S)}{\sqrt{\sum_{w \in S} V'(w, S)^2}} \\ \\ V'(w, S) &= log(1+TF_{w,S}) \cdot log(1+IDF_w) \end{array}\end{split}\]

Notes

One is added to both the TF & IDF values before taking the logarithm to ensure the logarithms do not fall to 0, which will tend to result in 0.0 similarities even when there is a degree of matching.

Rather than needing to exceed the threshold value, as in [CRF03] the similarity must be greater than or equal to the threshold.

New in version 0.4.0.

Initialize SoftTFIDF instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • corpus (UnigramCorpus) -- A unigram corpus UnigramCorpus. If None, a corpus will be created from the two words when a similarity function is called.

  • metric (_Distance) -- A string distance measure class for making soft matches, by default Jaro-Winkler.

  • threshold (float) -- A threshold value, similarities above which are counted as soft matches, by default 0.9.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the SoftTF-IDF similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

SoftTF-IDF similarity

Return type

float

Examples

>>> cmp = SoftTFIDF()
>>> cmp.sim('cat', 'hat')
0.30404449697373
>>> cmp.sim('Niall', 'Neil')
0.20108911303601
>>> cmp.sim('aluminum', 'Catalan')
0.05355175631194
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.JensenShannon(tokenizer=None, intersection_type='crisp', **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Jensen-Shannon divergence.

Jensen-Shannon divergence [DLP99] of two multi-sets X and Y is

\[ \begin{align}\begin{aligned}\begin{array}{rl} dist_{JS}(X, Y) &= log 2 + \frac{1}{2} \sum_{i \in X \cap Y} h(p(X_i) + p(Y_i)) - h(p(X_i)) - h(p(Y_i))\\h(x) &= -x log x\\p(X_i \in X) &= \frac{|X_i|}{|X|} \end{array}\end{aligned}\end{align} \]

New in version 0.4.0.

Initialize JensenShannon instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Jensen-Shannon distance of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Jensen-Shannon distance

Return type

float

Examples

>>> cmp = JensenShannon()
>>> cmp.dist('cat', 'hat')
0.49999999999999994
>>> cmp.dist('Niall', 'Neil')
0.6355222557917826
>>> cmp.dist('aluminum', 'Catalan')
0.8822392827203127
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Jensen-Shannon divergence of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Jensen-Shannon divergence

Return type

float

Examples

>>> cmp = JensenShannon()
>>> cmp.dist_abs('cat', 'hat')
0.3465735902799726
>>> cmp.dist_abs('Niall', 'Neil')
0.44051045978517045
>>> cmp.dist_abs('aluminum', 'Catalan')
0.6115216713968132
>>> cmp.dist_abs('ATCG', 'TAGC')
0.6931471805599453

New in version 0.4.0.

class abydos.distance.FellegiSunter(tokenizer=None, intersection_type='crisp', simplified=False, mismatch_factor=0.5, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

Fellegi-Sunter similarity.

Fellegi-Sunter similarity is based on the description in [CRF03] and implementation in [CRFR03].

New in version 0.4.0.

Initialize FellegiSunter instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • intersection_type (str) -- Specifies the intersection type, and set type as a result: See intersection_type description in _TokenDistance for details.

  • simplified (bool) -- Specifies to use the simplified scoring variant

  • mismatch_factor (float) -- Specifies the penalty factor for mismatches

  • **kwargs -- Arbitrary keyword arguments

Other Parameters
  • qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

  • metric (_Distance) -- A string distance measure class for use in the soft and fuzzy variants.

  • threshold (float) -- A threshold value, similarities above which are counted as members of the intersection for the fuzzy variant.

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Fellegi-Sunter similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized Fellegi-Sunter similarity

Return type

float

Examples

>>> cmp = FellegiSunter()
>>> cmp.sim('cat', 'hat')
0.2934477792670495
>>> cmp.sim('Niall', 'Neil')
0.13917536933271363
>>> cmp.sim('aluminum', 'Catalan')
0.056763632331436484
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

sim_score(src, tar)[source]

Return the Fellegi-Sunter similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Fellegi-Sunter similarity

Return type

float

Examples

>>> cmp = FellegiSunter()
>>> cmp.sim_score('cat', 'hat')
0.8803433378011485
>>> cmp.sim_score('Niall', 'Neil')
0.6958768466635681
>>> cmp.sim_score('aluminum', 'Catalan')
0.45410905865149187
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.MinHash(tokenizer=None, k=0, seed=10, **kwargs)[source]

Bases: abydos.distance._distance._Distance

MinHash similarity.

MinHash similarity [Bro97] is a method of approximating the intersection over the union of two sets. This implementation is based on [Kul15].

New in version 0.4.0.

Initialize MinHash instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • k (int) -- The number of hash functions to use for similarity estimation

  • seed (int) -- A seed value for the random functions

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the MinHash similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

MinHash similarity

Return type

float

Examples

>>> cmp = MinHash()
>>> cmp.sim('cat', 'hat')
0.75
>>> cmp.sim('Niall', 'Neil')
1.0
>>> cmp.sim('aluminum', 'Catalan')
0.5
>>> cmp.sim('ATCG', 'TAGC')
0.6

New in version 0.4.0.

class abydos.distance.BLEU(n_min=1, n_max=4, tokenizers=None, weights=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

BLEU similarity.

BLEU similarity [PRWZ02] compares two strings for similarity using a set of tokenizers and a brevity penalty:

\[\begin{split}BP = \left\{ \begin{array}{lrl} 1 & \textup{if} & c > r \\ e^{(1-\frac{r}{c})} & \textup{if} & c \leq r \end{array} \right.\end{split}\]

The BLEU score is then:

\[\textup{B\textsc{leu}} = BP \cdot e^{\sum_{n=1}^N w_n log p_n}\]

For tokenizers 1 to N, by default q-gram tokenizers for q=1 to N in Abydos, weights \(w_n\), which are uniformly \(\frac{1}{N}\), and \(p_n\):

\[p_n = \frac{\sum_{token \in tar} min(Count(token \in tar), Count(token \in src))}{|tar|}\]

New in version 0.4.0.

Initialize BLEU instance.

Parameters
  • n_min (int) -- The minimum q-gram value for BLEU score calculation (1 by default)

  • n_max (int) -- The maximum q-gram value for BLEU score calculation (4 by default)

  • tokenizers (list(_Tokenizer)) -- A list of initialized tokenizers

  • weights (list(float)) -- A list of floats representing the weights of the tokenizers. If tokenizers is set, this must have the same length. If n_min and n_max are used to set tokenizers, this must have length equal to n_max-n_min-1. Otherwise, uniform weights will be used.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the BLEU similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

BLEU similarity

Return type

float

Examples

>>> cmp = BLEU()
>>> cmp.sim('cat', 'hat')
0.7598356856515925
>>> cmp.sim('Niall', 'Neil')
0.7247557929987696
>>> cmp.sim('aluminum', 'Catalan')
0.44815260192961937
>>> cmp.sim('ATCG', 'TAGC')
1.0

New in version 0.4.0.

class abydos.distance.RougeL(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Rouge-L similarity.

Rouge-L similarity [Lin04]

New in version 0.4.0.

Initialize RougeL instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar, beta=8)[source]

Return the Rouge-L similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • beta (int or float) -- A weighting factor to prejudice similarity towards src

Returns

Rouge-L similarity

Return type

float

Examples

>>> cmp = RougeL()
>>> cmp.sim('cat', 'hat')
0.6666666666666666
>>> cmp.sim('Niall', 'Neil')
0.6018518518518519
>>> cmp.sim('aluminum', 'Catalan')
0.3757225433526012
>>> cmp.sim('ATCG', 'TAGC')
0.5

New in version 0.4.0.

class abydos.distance.RougeW(f_func=None, f_inv=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Rouge-W similarity.

Rouge-W similarity [Lin04]

New in version 0.4.0.

Initialize RougeW instance.

Parameters
  • f_func (function) -- A weighting function based on the value supplied to this function, such that f(x+y) > f(x) + f(y)

  • f_inv (function) -- The close form inverse of f_func

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar, beta=8)[source]

Return the Rouge-W similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • beta (int or float) -- A weighting factor to prejudice similarity towards src

Returns

Rouge-W similarity

Return type

float

Examples

>>> cmp = RougeW()
>>> cmp.sim('cat', 'hat')
0.6666666666666666
>>> cmp.sim('Niall', 'Neil')
0.34747932867894143
>>> cmp.sim('aluminum', 'Catalan')
0.280047049205176
>>> cmp.sim('ATCG', 'TAGC')
0.43301270189221935

New in version 0.4.0.

wlcs(src, tar)[source]

Return the Rouge-W weighted longest common sub-sequence length.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Levenshtein distance between src & tar

Return type

int (may return a float if cost has float values)

Examples

>>> cmp = RougeW()
>>> cmp.wlcs('cat', 'hat')
4
>>> cmp.wlcs('Niall', 'Neil')
3
>>> cmp.wlcs('aluminum', 'Catalan')
5
>>> cmp.wlcs('ATCG', 'TAGC')
3

New in version 0.4.0.

class abydos.distance.RougeS(qval=2, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Rouge-S similarity.

Rouge-S similarity [Lin04], operating on character-level skipgrams

New in version 0.4.0.

Initialize RougeS instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar, beta=8)[source]

Return the Rouge-S similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • beta (int or float) -- A weighting factor to prejudice similarity towards src

Returns

Rouge-S similarity

Return type

float

Examples

>>> cmp = RougeS()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.30185758513931893
>>> cmp.sim('aluminum', 'Catalan')
0.10755653612796467
>>> cmp.sim('ATCG', 'TAGC')
0.6666666666666666

New in version 0.4.0.

class abydos.distance.RougeSU(qval=2, **kwargs)[source]

Bases: abydos.distance._rouge_s.RougeS

Rouge-SU similarity.

Rouge-SU similarity [Lin04], operating on character-level skipgrams

New in version 0.4.0.

Initialize RougeSU instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar, beta=8)[source]

Return the Rouge-SU similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • beta (int or float) -- A weighting factor to prejudice similarity towards src

Returns

Rouge-SU similarity

Return type

float

Examples

>>> cmp = RougeSU()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.4020618556701031
>>> cmp.sim('aluminum', 'Catalan')
0.1672384219554031
>>> cmp.sim('ATCG', 'TAGC')
0.8

New in version 0.4.0.

class abydos.distance.PositionalQGramDice(max_dist=1, tokenizer=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Positional Q-Gram Dice coefficient.

Positional Q-Gram Dice coefficient [GIJ+01][Chr06]

New in version 0.4.0.

Initialize PositionalQGramDice instance.

Parameters
  • max_dist (int) -- The maximum positional distance between to q-grams to count as a match.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Positional Q-Gram Dice coefficient of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Positional Q-Gram Dice coefficient

Return type

float

Examples

>>> cmp = PositionalQGramDice()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.36363636363636365
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.PositionalQGramJaccard(max_dist=1, tokenizer=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Positional Q-Gram Jaccard coefficient.

Positional Q-Gram Jaccard coefficient [GIJ+01][Chr06]

New in version 0.4.0.

Initialize PositionalQGramJaccard instance.

Parameters
  • max_dist (int) -- The maximum positional distance between to q-grams to count as a match.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Positional Q-Gram Jaccard coefficient of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Positional Q-Gram Jaccard coefficient

Return type

float

Examples

>>> cmp = PositionalQGramJaccard()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.2222222222222222
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.PositionalQGramOverlap(max_dist=1, tokenizer=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Positional Q-Gram Overlap coefficient.

Positional Q-Gram Overlap coefficient [GIJ+01][Chr06]

New in version 0.4.0.

Initialize PositionalQGramOverlap instance.

Parameters
  • max_dist (int) -- The maximum positional distance between to q-grams to count as a match.

  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the Positional Q-Gram Overlap coefficient of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Positional Q-Gram Overlap coefficient

Return type

float

Examples

>>> cmp = PositionalQGramOverlap()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.4
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.NeedlemanWunsch(gap_cost=1, sim_func=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Needleman-Wunsch score.

The Needleman-Wunsch score [NW70] is a standard edit distance measure.

New in version 0.3.6.

Initialize NeedlemanWunsch instance.

Parameters
  • gap_cost (float) -- The cost of an alignment gap (1 by default)

  • sim_func (function) -- A function that returns the similarity of two characters (identity similarity by default)

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Needleman-Wunsch score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Needleman-Wunsch score

Return type

float

Examples

>>> cmp = NeedlemanWunsch()
>>> cmp.sim('cat', 'hat')
0.6666666666666667
>>> cmp.sim('Niall', 'Neil')
0.22360679774997896
>>> round(cmp.sim('aluminum', 'Catalan'), 12)
0.0
>>> cmp.sim('cat', 'hat')
0.6666666666666667

New in version 0.4.1.

static sim_matrix(src, tar, mat=None, mismatch_cost=0, match_cost=1, symmetric=True, alphabet=None)[source]

Return the matrix similarity of two strings.

With the default parameters, this is identical to sim_ident. It is possible for sim_matrix to return values outside of the range \([0, 1]\), if values outside that range are present in mat, mismatch_cost, or match_cost.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • mat (dict) -- A dict mapping tuples to costs; the tuples are (src, tar) pairs of symbols from the alphabet parameter

  • mismatch_cost (float) -- The value returned if (src, tar) is absent from mat when src does not equal tar

  • match_cost (float) -- The value returned if (src, tar) is absent from mat when src equals tar

  • symmetric (bool) -- True if the cost of src not matching tar is identical to the cost of tar not matching src; in this case, the values in mat need only contain (src, tar) or (tar, src), not both

  • alphabet (str) -- A collection of tokens from which src and tar are drawn; if this is defined a ValueError is raised if either tar or src is not found in alphabet

Returns

Matrix similarity

Return type

float

Raises
  • ValueError -- src value not in alphabet

  • ValueError -- tar value not in alphabet

Examples

>>> NeedlemanWunsch.sim_matrix('cat', 'hat')
0
>>> NeedlemanWunsch.sim_matrix('hat', 'hat')
1

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

sim_score(src, tar)[source]

Return the Needleman-Wunsch score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Needleman-Wunsch score

Return type

float

Examples

>>> cmp = NeedlemanWunsch()
>>> cmp.sim_score('cat', 'hat')
2.0
>>> cmp.sim_score('Niall', 'Neil')
1.0
>>> cmp.sim_score('aluminum', 'Catalan')
-1.0
>>> cmp.sim_score('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.needleman_wunsch(src, tar, gap_cost=1, sim_func=<function sim_ident>)[source]

Return the Needleman-Wunsch score of two strings.

This is a wrapper for NeedlemanWunsch.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • gap_cost (float) -- The cost of an alignment gap (1 by default)

  • sim_func (function) -- A function that returns the similarity of two characters (identity similarity by default)

Returns

Needleman-Wunsch score

Return type

float

Examples

>>> needleman_wunsch('cat', 'hat')
2.0
>>> needleman_wunsch('Niall', 'Neil')
1.0
>>> needleman_wunsch('aluminum', 'Catalan')
-1.0
>>> needleman_wunsch('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NeedlemanWunsch.dist_abs method instead.

class abydos.distance.SmithWaterman(gap_cost=1, sim_func=None, **kwargs)[source]

Bases: abydos.distance._needleman_wunsch.NeedlemanWunsch

Smith-Waterman score.

The Smith-Waterman score [SW81] is a standard edit distance measure, differing from Needleman-Wunsch in that it focuses on local alignment and disallows negative scores.

New in version 0.3.6.

Initialize SmithWaterman instance.

Parameters
  • gap_cost (float) -- The cost of an alignment gap (1 by default)

  • sim_func (function) -- A function that returns the similarity of two characters (identity similarity by default)

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Smith-Waterman score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Smith-Waterman score

Return type

float

Examples

>>> cmp = SmithWaterman()
>>> cmp.sim('cat', 'hat')
0.6666666666666667
>>> cmp.sim('Niall', 'Neil')
0.22360679774997896
>>> round(cmp.sim('aluminum', 'Catalan'), 12)
0.0
>>> cmp.sim('cat', 'hat')
0.6666666666666667

New in version 0.4.1.

sim_score(src, tar)[source]

Return the Smith-Waterman score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Smith-Waterman score

Return type

float

Examples

>>> cmp = SmithWaterman()
>>> cmp.sim_score('cat', 'hat')
2.0
>>> cmp.sim_score('Niall', 'Neil')
1.0
>>> cmp.sim_score('aluminum', 'Catalan')
0.0
>>> cmp.sim_score('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.smith_waterman(src, tar, gap_cost=1, sim_func=<function sim_ident>)[source]

Return the Smith-Waterman score of two strings.

This is a wrapper for SmithWaterman.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • gap_cost (float) -- The cost of an alignment gap (1 by default)

  • sim_func (function) -- A function that returns the similarity of two characters (identity similarity by default)

Returns

Smith-Waterman score

Return type

float

Examples

>>> smith_waterman('cat', 'hat')
2.0
>>> smith_waterman('Niall', 'Neil')
1.0
>>> smith_waterman('aluminum', 'Catalan')
0.0
>>> smith_waterman('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the SmithWaterman.dist_abs method instead.

class abydos.distance.Gotoh(gap_open=1, gap_ext=0.4, sim_func=None, **kwargs)[source]

Bases: abydos.distance._needleman_wunsch.NeedlemanWunsch

Gotoh score.

The Gotoh score [Got82] is essentially Needleman-Wunsch with affine gap penalties.

New in version 0.3.6.

Initialize Gotoh instance.

Parameters
  • gap_open (float) -- The cost of an open alignment gap (1 by default)

  • gap_ext (float) -- The cost of an alignment gap extension (0.4 by default)

  • sim_func (function) -- A function that returns the similarity of two characters (identity similarity by default)

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the normalized Gotoh score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Gotoh score

Return type

float

Examples

>>> cmp = Gotoh()
>>> cmp.sim('cat', 'hat')
0.6666666666666667
>>> cmp.sim('Niall', 'Neil')
0.22360679774997896
>>> round(cmp.sim('aluminum', 'Catalan'), 12)
0.0
>>> cmp.sim('cat', 'hat')
0.6666666666666667

New in version 0.4.1.

sim_score(src, tar)[source]

Return the Gotoh score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Gotoh score

Return type

float

Examples

>>> cmp = Gotoh()
>>> cmp.sim_score('cat', 'hat')
2.0
>>> cmp.sim_score('Niall', 'Neil')
1.0
>>> round(cmp.sim_score('aluminum', 'Catalan'), 12)
-0.4
>>> cmp.sim_score('cat', 'hat')
2.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.gotoh(src, tar, gap_open=1, gap_ext=0.4, sim_func=<function sim_ident>)[source]

Return the Gotoh score of two strings.

This is a wrapper for Gotoh.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • gap_open (float) -- The cost of an open alignment gap (1 by default)

  • gap_ext (float) -- The cost of an alignment gap extension (0.4 by default)

  • sim_func (function) -- A function that returns the similarity of two characters (identity similarity by default)

Returns

Gotoh score

Return type

float

Examples

>>> gotoh('cat', 'hat')
2.0
>>> gotoh('Niall', 'Neil')
1.0
>>> round(gotoh('aluminum', 'Catalan'), 12)
-0.4
>>> gotoh('cat', 'hat')
2.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Gotoh.dist_abs method instead.

class abydos.distance.LCSseq(normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Longest common subsequence.

Longest common subsequence (LCSseq) is the longest subsequence of characters that two strings have in common.

New in version 0.3.6.

Initialize LCSseq.

Parameters
  • normalizer (function) -- A normalization function for the normalized similarity & distance. By default, the max of the lengths of the input strings. If lambda x: sum(x)/2.0 is supplied, the normalization proposed in [RTS+01] is used, i.e. \(\frac{2 \dot |LCS(src, tar)|}{|src| + |tar|}\).

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

lcsseq(src, tar)[source]

Return the longest common subsequence of two strings.

Based on the dynamic programming algorithm from http://rosettacode.org/wiki/Longest_common_subsequence [Cod18a]. This is licensed GFDL 1.2.

Modifications include:

conversion to a numpy array in place of a list of lists

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The longest common subsequence

Return type

str

Examples

>>> sseq = LCSseq()
>>> sseq.lcsseq('cat', 'hat')
'at'
>>> sseq.lcsseq('Niall', 'Neil')
'Nil'
>>> sseq.lcsseq('aluminum', 'Catalan')
'aln'
>>> sseq.lcsseq('ATCG', 'TAGC')
'AC'

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

sim(src, tar)[source]

Return the longest common subsequence similarity of two strings.

Longest common subsequence similarity (\(sim_{LCSseq}\)).

This employs the LCSseq function to derive a similarity metric: \(sim_{LCSseq}(s,t) = \frac{|LCSseq(s,t)|}{max(|s|, |t|)}\)

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

LCSseq similarity

Return type

float

Examples

>>> sseq = LCSseq()
>>> sseq.sim('cat', 'hat')
0.6666666666666666
>>> sseq.sim('Niall', 'Neil')
0.6
>>> sseq.sim('aluminum', 'Catalan')
0.375
>>> sseq.sim('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

Changed in version 0.4.0: Added normalization option

abydos.distance.lcsseq(src, tar)[source]

Return the longest common subsequence of two strings.

This is a wrapper for LCSseq.lcsseq().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The longest common subsequence

Return type

str

Examples

>>> lcsseq('cat', 'hat')
'at'
>>> lcsseq('Niall', 'Neil')
'Nil'
>>> lcsseq('aluminum', 'Catalan')
'aln'
>>> lcsseq('ATCG', 'TAGC')
'AC'

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the LCSseq.lcsseq method instead.

abydos.distance.dist_lcsseq(src, tar)[source]

Return the longest common subsequence distance between two strings.

This is a wrapper for LCSseq.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

LCSseq distance

Return type

float

Examples

>>> dist_lcsseq('cat', 'hat')
0.33333333333333337
>>> dist_lcsseq('Niall', 'Neil')
0.4
>>> dist_lcsseq('aluminum', 'Catalan')
0.625
>>> dist_lcsseq('ATCG', 'TAGC')
0.5

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the LCSseq.dist method instead.

abydos.distance.sim_lcsseq(src, tar)[source]

Return the longest common subsequence similarity of two strings.

This is a wrapper for LCSseq.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

LCSseq similarity

Return type

float

Examples

>>> sim_lcsseq('cat', 'hat')
0.6666666666666666
>>> sim_lcsseq('Niall', 'Neil')
0.6
>>> sim_lcsseq('aluminum', 'Catalan')
0.375
>>> sim_lcsseq('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the LCSseq.sim method instead.

class abydos.distance.LCSstr(normalizer=<built-in function max>, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Longest common substring.

New in version 0.3.6.

Initialize LCSseq.

Parameters
  • normalizer (function) -- A normalization function for the normalized similarity & distance. By default, the max of the lengths of the input strings. If lambda x: sum(x)/2.0 is supplied, the normalization proposed in [RTS+01] is used, i.e. \(\frac{2 \dot |LCS(src, tar)|}{|src| + |tar|}\).

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

lcsstr(src, tar)[source]

Return the longest common substring of two strings.

Longest common substring (LCSstr).

Based on the code from https://en.wikibooks.org/wiki/Algorithm_Implementation/Strings/Longest_common_substring [Wik18]. This is licensed Creative Commons: Attribution-ShareAlike 3.0.

Modifications include:

  • conversion to a numpy array in place of a list of lists

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The longest common substring

Return type

str

Examples

>>> sstr = LCSstr()
>>> sstr.lcsstr('cat', 'hat')
'at'
>>> sstr.lcsstr('Niall', 'Neil')
'N'
>>> sstr.lcsstr('aluminum', 'Catalan')
'al'
>>> sstr.lcsstr('ATCG', 'TAGC')
'A'

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

sim(src, tar)[source]

Return the longest common substring similarity of two strings.

Longest common substring similarity (\(sim_{LCSstr}\)).

This employs the LCS function to derive a similarity metric: \(sim_{LCSstr}(s,t) = \frac{|LCSstr(s,t)|}{max(|s|, |t|)}\)

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

LCSstr similarity

Return type

float

Examples

>>> sstr = LCSstr()
>>> sstr.sim('cat', 'hat')
0.6666666666666666
>>> sstr.sim('Niall', 'Neil')
0.2
>>> sstr.sim('aluminum', 'Catalan')
0.25
>>> sstr.sim('ATCG', 'TAGC')
0.25

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

Changed in version 0.4.0: Added normalization option

abydos.distance.lcsstr(src, tar)[source]

Return the longest common substring of two strings.

This is a wrapper for LCSstr.lcsstr().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The longest common substring

Return type

str

Examples

>>> lcsstr('cat', 'hat')
'at'
>>> lcsstr('Niall', 'Neil')
'N'
>>> lcsstr('aluminum', 'Catalan')
'al'
>>> lcsstr('ATCG', 'TAGC')
'A'

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the LCSstr.lcsstr method instead.

abydos.distance.dist_lcsstr(src, tar)[source]

Return the longest common substring distance between two strings.

This is a wrapper for LCSstr.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

LCSstr distance

Return type

float

Examples

>>> dist_lcsstr('cat', 'hat')
0.33333333333333337
>>> dist_lcsstr('Niall', 'Neil')
0.8
>>> dist_lcsstr('aluminum', 'Catalan')
0.75
>>> dist_lcsstr('ATCG', 'TAGC')
0.75

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the LCSstr.dist method instead.

abydos.distance.sim_lcsstr(src, tar)[source]

Return the longest common substring similarity of two strings.

This is a wrapper for LCSstr.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

LCSstr similarity

Return type

float

Examples

>>> sim_lcsstr('cat', 'hat')
0.6666666666666666
>>> sim_lcsstr('Niall', 'Neil')
0.2
>>> sim_lcsstr('aluminum', 'Catalan')
0.25
>>> sim_lcsstr('ATCG', 'TAGC')
0.25

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the LCSstr.sim method instead.

class abydos.distance.LCPrefix(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Longest common prefix.

New in version 0.4.0.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist_abs(src, tar, *args)[source]

Return the length of the longest common prefix of the strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • *args (strs) -- Additional strings for comparison

Raises

ValueError -- All arguments must be of type str

Returns

The length of the longest common prefix

Return type

int

Examples

>>> pfx = LCPrefix()
>>> pfx.dist_abs('cat', 'hat')
0
>>> pfx.dist_abs('Niall', 'Neil')
1
>>> pfx.dist_abs('aluminum', 'Catalan')
0
>>> pfx.dist_abs('ATCG', 'TAGC')
0

New in version 0.4.0.

lcprefix(strings)[source]

Return the longest common prefix of a list of strings.

Longest common prefix (LCPrefix).

Parameters

strings (list of strings) -- Strings for comparison

Returns

The longest common prefix

Return type

str

Examples

>>> pfx = LCPrefix()
>>> pfx.lcprefix(['cat', 'hat'])
''
>>> pfx.lcprefix(['Niall', 'Neil'])
'N'
>>> pfx.lcprefix(['aluminum', 'Catalan'])
''
>>> pfx.lcprefix(['ATCG', 'TAGC'])
''

New in version 0.4.0.

sim(src, tar, *args)[source]

Return the longest common prefix similarity of two or more strings.

Longest common prefix similarity (\(sim_{LCPrefix}\)).

This employs the LCPrefix function to derive a similarity metric: \(sim_{LCPrefix}(s,t) = \frac{|LCPrefix(s,t)|}{max(|s|, |t|)}\)

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • *args (strs) -- Additional strings for comparison

Returns

LCPrefix similarity

Return type

float

Examples

>>> pfx = LCPrefix()
>>> pfx.sim('cat', 'hat')
0.0
>>> pfx.sim('Niall', 'Neil')
0.2
>>> pfx.sim('aluminum', 'Catalan')
0.0
>>> pfx.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.LCSuffix(**kwargs)[source]

Bases: abydos.distance._lcprefix.LCPrefix

Longest common suffix.

New in version 0.4.0.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist_abs(src, tar, *args)[source]

Return the length of the longest common suffix of the strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • *args (strs) -- Additional strings for comparison

Raises

ValueError -- All arguments must be of type str

Returns

The length of the longest common suffix

Return type

int

Examples

>>> sfx = LCSuffix()
>>> sfx.dist_abs('cat', 'hat')
2
>>> sfx.dist_abs('Niall', 'Neil')
1
>>> sfx.dist_abs('aluminum', 'Catalan')
0
>>> sfx.dist_abs('ATCG', 'TAGC')
0

New in version 0.4.0.

lcsuffix(strings)[source]

Return the longest common suffix of a list of strings.

Longest common suffix (LCSuffix).

Parameters

strings (list of strings) -- Strings for comparison

Returns

The longest common suffix

Return type

str

Examples

>>> sfx = LCSuffix()
>>> sfx.lcsuffix(['cat', 'hat'])
'at'
>>> sfx.lcsuffix(['Niall', 'Neil'])
'l'
>>> sfx.lcsuffix(['aluminum', 'Catalan'])
''
>>> sfx.lcsuffix(['ATCG', 'TAGC'])
''

New in version 0.4.0.

sim(src, tar, *args)[source]

Return the longest common suffix similarity of two or more strings.

Longest common prefix similarity (\(sim_{LCPrefix}\)).

This employs the LCSuffix function to derive a similarity metric: \(sim_{LCSuffix}(s,t) = \frac{|LCSuffix(s,t)|}{max(|s|, |t|)}\)

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • *args (strs) -- Additional strings for comparison

Returns

LCSuffix similarity

Return type

float

Examples

>>> pfx = LCPrefix()
>>> pfx.sim('cat', 'hat')
0.0
>>> pfx.sim('Niall', 'Neil')
0.2
>>> pfx.sim('aluminum', 'Catalan')
0.0
>>> pfx.sim('ATCG', 'TAGC')
0.0

New in version 0.4.0.

class abydos.distance.RatcliffObershelp(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Ratcliff-Obershelp similarity.

This follows the Ratcliff-Obershelp algorithm [RM88] to derive a similarity measure:

  1. Find the length of the longest common substring in src & tar.

  2. Recurse on the strings to the left & right of each this substring in src & tar. The base case is a 0 length common substring, in which case, return 0. Otherwise, return the sum of the current longest common substring and the left & right recursed sums.

  3. Multiply this length by 2 and divide by the sum of the lengths of src & tar.

Cf. http://www.drdobbs.com/database/pattern-matching-the-gestalt-approach/184407970

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the Ratcliff-Obershelp similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Ratcliff-Obershelp similarity

Return type

float

Examples

>>> cmp = RatcliffObershelp()
>>> round(cmp.sim('cat', 'hat'), 12)
0.666666666667
>>> round(cmp.sim('Niall', 'Neil'), 12)
0.666666666667
>>> round(cmp.sim('aluminum', 'Catalan'), 12)
0.4
>>> cmp.sim('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ratcliff_obershelp(src, tar)[source]

Return the Ratcliff-Obershelp distance between two strings.

This is a wrapper for RatcliffObershelp.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Ratcliff-Obershelp distance

Return type

float

Examples

>>> round(dist_ratcliff_obershelp('cat', 'hat'), 12)
0.333333333333
>>> round(dist_ratcliff_obershelp('Niall', 'Neil'), 12)
0.333333333333
>>> round(dist_ratcliff_obershelp('aluminum', 'Catalan'), 12)
0.6
>>> dist_ratcliff_obershelp('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the RatcliffObershelp.dist method instead.

abydos.distance.sim_ratcliff_obershelp(src, tar)[source]

Return the Ratcliff-Obershelp similarity of two strings.

This is a wrapper for RatcliffObershelp.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Ratcliff-Obershelp similarity

Return type

float

Examples

>>> round(sim_ratcliff_obershelp('cat', 'hat'), 12)
0.666666666667
>>> round(sim_ratcliff_obershelp('Niall', 'Neil'), 12)
0.666666666667
>>> round(sim_ratcliff_obershelp('aluminum', 'Catalan'), 12)
0.4
>>> sim_ratcliff_obershelp('ATCG', 'TAGC')
0.5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the RatcliffObershelp.sim method instead.

class abydos.distance.Ident(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Identity distance and similarity.

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the identity similarity of two strings.

Identity similarity is 1.0 if the two strings are identical, otherwise 0.0

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Identity similarity

Return type

float

Examples

>>> cmp = Ident()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('cat', 'cat')
1.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ident(src, tar)[source]

Return the identity distance between two strings.

This is a wrapper for Ident.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Identity distance

Return type

float

Examples

>>> dist_ident('cat', 'hat')
1.0
>>> dist_ident('cat', 'cat')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Ident.dist method instead.

abydos.distance.sim_ident(src, tar)[source]

Return the identity similarity of two strings.

This is a wrapper for Ident.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Identity similarity

Return type

float

Examples

>>> sim_ident('cat', 'hat')
0.0
>>> sim_ident('cat', 'cat')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Ident.sim method instead.

class abydos.distance.Length(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Length similarity and distance.

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the length similarity of two strings.

Length similarity is the ratio of the length of the shorter string to the longer.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Length similarity

Return type

float

Examples

>>> cmp = Length()
>>> cmp.sim('cat', 'hat')
1.0
>>> cmp.sim('Niall', 'Neil')
0.8
>>> cmp.sim('aluminum', 'Catalan')
0.875
>>> cmp.sim('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_length(src, tar)[source]

Return the length distance between two strings.

This is a wrapper for Length.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Length distance

Return type

float

Examples

>>> dist_length('cat', 'hat')
0.0
>>> dist_length('Niall', 'Neil')
0.19999999999999996
>>> dist_length('aluminum', 'Catalan')
0.125
>>> dist_length('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Length.dist method instead.

abydos.distance.sim_length(src, tar)[source]

Return the length similarity of two strings.

This is a wrapper for Length.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Length similarity

Return type

float

Examples

>>> sim_length('cat', 'hat')
1.0
>>> sim_length('Niall', 'Neil')
0.8
>>> sim_length('aluminum', 'Catalan')
0.875
>>> sim_length('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Length.sim method instead.

class abydos.distance.Prefix(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Prefix similiarity and distance.

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the prefix similarity of two strings.

Prefix similarity is the ratio of the length of the shorter term that exactly matches the longer term to the length of the shorter term, beginning at the start of both terms.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Prefix similarity

Return type

float

Examples

>>> cmp = Prefix()
>>> cmp.sim('cat', 'hat')
0.0
>>> cmp.sim('Niall', 'Neil')
0.25
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_prefix(src, tar)[source]

Return the prefix distance between two strings.

This is a wrapper for Prefix.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Prefix distance

Return type

float

Examples

>>> dist_prefix('cat', 'hat')
1.0
>>> dist_prefix('Niall', 'Neil')
0.75
>>> dist_prefix('aluminum', 'Catalan')
1.0
>>> dist_prefix('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Prefix.dist method instead.

abydos.distance.sim_prefix(src, tar)[source]

Return the prefix similarity of two strings.

This is a wrapper for Prefix.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Prefix similarity

Return type

float

Examples

>>> sim_prefix('cat', 'hat')
0.0
>>> sim_prefix('Niall', 'Neil')
0.25
>>> sim_prefix('aluminum', 'Catalan')
0.0
>>> sim_prefix('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Prefix.sim method instead.

class abydos.distance.Suffix(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Suffix similarity and distance.

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the suffix similarity of two strings.

Suffix similarity is the ratio of the length of the shorter term that exactly matches the longer term to the length of the shorter term, beginning at the end of both terms.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Suffix similarity

Return type

float

Examples

>>> cmp = Suffix()
>>> cmp.sim('cat', 'hat')
0.6666666666666666
>>> cmp.sim('Niall', 'Neil')
0.25
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_suffix(src, tar)[source]

Return the suffix distance between two strings.

This is a wrapper for Suffix.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Suffix distance

Return type

float

Examples

>>> dist_suffix('cat', 'hat')
0.33333333333333337
>>> dist_suffix('Niall', 'Neil')
0.75
>>> dist_suffix('aluminum', 'Catalan')
1.0
>>> dist_suffix('ATCG', 'TAGC')
1.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Suffix.dist method instead.

abydos.distance.sim_suffix(src, tar)[source]

Return the suffix similarity of two strings.

This is a wrapper for Suffix.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Suffix similarity

Return type

float

Examples

>>> sim_suffix('cat', 'hat')
0.6666666666666666
>>> sim_suffix('Niall', 'Neil')
0.25
>>> sim_suffix('aluminum', 'Catalan')
0.0
>>> sim_suffix('ATCG', 'TAGC')
0.0

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Suffix.sim method instead.

class abydos.distance.NCDzlib(level=-1, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using zlib compression.

Cf. https://zlib.net/

Normalized compression distance (NCD) [CV05].

New in version 0.3.6.

Initialize zlib compressor.

Parameters

level (int) -- The compression level (0 to 9)

New in version 0.3.6.

dist(src, tar)[source]

Return the NCD between two strings using zlib compression.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> cmp = NCDzlib()
>>> cmp.dist('cat', 'hat')
0.3333333333333333
>>> cmp.dist('Niall', 'Neil')
0.45454545454545453
>>> cmp.dist('aluminum', 'Catalan')
0.5714285714285714
>>> cmp.dist('ATCG', 'TAGC')
0.4

New in version 0.3.5.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ncd_zlib(src, tar)[source]

Return the NCD between two strings using zlib compression.

This is a wrapper for NCDzlib.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> dist_ncd_zlib('cat', 'hat')
0.3333333333333333
>>> dist_ncd_zlib('Niall', 'Neil')
0.45454545454545453
>>> dist_ncd_zlib('aluminum', 'Catalan')
0.5714285714285714
>>> dist_ncd_zlib('ATCG', 'TAGC')
0.4

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDzlib.dist method instead.

abydos.distance.sim_ncd_zlib(src, tar)[source]

Return the NCD similarity between two strings using zlib compression.

This is a wrapper for NCDzlib.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

float

Return type

Compression similarity

Examples

>>> sim_ncd_zlib('cat', 'hat')
0.6666666666666667
>>> sim_ncd_zlib('Niall', 'Neil')
0.5454545454545454
>>> sim_ncd_zlib('aluminum', 'Catalan')
0.4285714285714286
>>> sim_ncd_zlib('ATCG', 'TAGC')
0.6

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDzlib.sim method instead.

class abydos.distance.NCDbz2(level=9, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using bzip2 compression.

Cf. https://en.wikipedia.org/wiki/Bzip2

Normalized compression distance (NCD) [CV05].

New in version 0.3.6.

Initialize bzip2 compressor.

Parameters

level (int) -- The compression level (0 to 9)

New in version 0.3.6.

Changed in version 0.3.6: Encapsulated in class

dist(src, tar)[source]

Return the NCD between two strings using bzip2 compression.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> cmp = NCDbz2()
>>> cmp.dist('cat', 'hat')
0.06666666666666667
>>> cmp.dist('Niall', 'Neil')
0.03125
>>> cmp.dist('aluminum', 'Catalan')
0.17647058823529413
>>> cmp.dist('ATCG', 'TAGC')
0.03125

New in version 0.3.5.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ncd_bz2(src, tar)[source]

Return the NCD between two strings using bzip2 compression.

This is a wrapper for NCDbz2.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> dist_ncd_bz2('cat', 'hat')
0.06666666666666667
>>> dist_ncd_bz2('Niall', 'Neil')
0.03125
>>> dist_ncd_bz2('aluminum', 'Catalan')
0.17647058823529413
>>> dist_ncd_bz2('ATCG', 'TAGC')
0.03125

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDbz2.dist method instead.

abydos.distance.sim_ncd_bz2(src, tar)[source]

Return the NCD similarity between two strings using bzip2 compression.

This is a wrapper for NCDbz2.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression similarity

Return type

float

Examples

>>> sim_ncd_bz2('cat', 'hat')
0.9333333333333333
>>> sim_ncd_bz2('Niall', 'Neil')
0.96875
>>> sim_ncd_bz2('aluminum', 'Catalan')
0.8235294117647058
>>> sim_ncd_bz2('ATCG', 'TAGC')
0.96875

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDbz2.sim method instead.

class abydos.distance.NCDlzma(level=6, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using LZMA compression.

Cf. https://en.wikipedia.org/wiki/Lempel-Ziv-Markov_chain_algorithm

Normalized compression distance (NCD) [CV05].

New in version 0.3.6.

Initialize LZMA compressor.

Parameters

level (int) -- The compression level (0 to 9)

New in version 0.5.0.

dist(src, tar)[source]

Return the NCD between two strings using LZMA compression.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> cmp = NCDlzma()
>>> cmp.dist('cat', 'hat')
0.08695652173913043
>>> cmp.dist('Niall', 'Neil')
0.16
>>> cmp.dist('aluminum', 'Catalan')
0.16
>>> cmp.dist('ATCG', 'TAGC')
0.08695652173913043

New in version 0.3.5.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ncd_lzma(src, tar)[source]

Return the NCD between two strings using LZMA compression.

This is a wrapper for NCDlzma.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> dist_ncd_lzma('cat', 'hat')
0.08695652173913043
>>> dist_ncd_lzma('Niall', 'Neil')
0.16
>>> dist_ncd_lzma('aluminum', 'Catalan')
0.16
>>> dist_ncd_lzma('ATCG', 'TAGC')
0.08695652173913043

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDlzma.dist method instead.

abydos.distance.sim_ncd_lzma(src, tar)[source]

Return the NCD similarity between two strings using LZMA compression.

This is a wrapper for NCDlzma.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression similarity

Return type

float

Examples

>>> sim_ncd_lzma('cat', 'hat')
0.9130434782608696
>>> sim_ncd_lzma('Niall', 'Neil')
0.84
>>> sim_ncd_lzma('aluminum', 'Catalan')
0.84
>>> sim_ncd_lzma('ATCG', 'TAGC')
0.9130434782608696

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDlzma.sim method instead.

class abydos.distance.NCDarith(probs=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using arithmetic coding.

Cf. https://en.wikipedia.org/wiki/Arithmetic_coding

Normalized compression distance (NCD) [CV05].

New in version 0.3.6.

Initialize the arithmetic coder object.

Parameters

probs (dict) -- A dictionary trained with Arithmetic.train()

New in version 0.3.6.

Changed in version 0.3.6: Encapsulated in class

dist(src, tar)[source]

Return the NCD between two strings using arithmetic coding.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> cmp = NCDarith()
>>> cmp.dist('cat', 'hat')
0.5454545454545454
>>> cmp.dist('Niall', 'Neil')
0.6875
>>> cmp.dist('aluminum', 'Catalan')
0.8275862068965517
>>> cmp.dist('ATCG', 'TAGC')
0.6923076923076923

New in version 0.3.5.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ncd_arith(src, tar, probs=None)[source]

Return the NCD between two strings using arithmetic coding.

This is a wrapper for NCDarith.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • probs (dict) -- A dictionary trained with Arithmetic.train()

Returns

Compression distance

Return type

float

Examples

>>> dist_ncd_arith('cat', 'hat')
0.5454545454545454
>>> dist_ncd_arith('Niall', 'Neil')
0.6875
>>> dist_ncd_arith('aluminum', 'Catalan')
0.8275862068965517
>>> dist_ncd_arith('ATCG', 'TAGC')
0.6923076923076923

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDarith.dist method instead.

abydos.distance.sim_ncd_arith(src, tar, probs=None)[source]

Return the NCD similarity between two strings using arithmetic coding.

This is a wrapper for NCDarith.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • probs (dict) -- A dictionary trained with Arithmetic.train()

Returns

Compression similarity

Return type

float

Examples

>>> sim_ncd_arith('cat', 'hat')
0.4545454545454546
>>> sim_ncd_arith('Niall', 'Neil')
0.3125
>>> sim_ncd_arith('aluminum', 'Catalan')
0.1724137931034483
>>> sim_ncd_arith('ATCG', 'TAGC')
0.3076923076923077

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDarith.sim method instead.

class abydos.distance.NCDbwtrle(**kwargs)[source]

Bases: abydos.distance._ncd_rle.NCDrle

Normalized Compression Distance using BWT plus RLE.

Cf. https://en.wikipedia.org/wiki/Burrows-Wheeler_transform

Normalized compression distance (NCD) [CV05].

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the NCD between two strings using BWT plus RLE.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> cmp = NCDbwtrle()
>>> cmp.dist('cat', 'hat')
0.75
>>> cmp.dist('Niall', 'Neil')
0.8333333333333334
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
0.8

New in version 0.3.5.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ncd_bwtrle(src, tar)[source]

Return the NCD between two strings using BWT plus RLE.

This is a wrapper for NCDbwtrle.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> dist_ncd_bwtrle('cat', 'hat')
0.75
>>> dist_ncd_bwtrle('Niall', 'Neil')
0.8333333333333334
>>> dist_ncd_bwtrle('aluminum', 'Catalan')
1.0
>>> dist_ncd_bwtrle('ATCG', 'TAGC')
0.8

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDbwtrle.dist method instead.

abydos.distance.sim_ncd_bwtrle(src, tar)[source]

Return the NCD similarity between two strings using BWT plus RLE.

This is a wrapper for NCDbwtrle.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression similarity

Return type

float

Examples

>>> sim_ncd_bwtrle('cat', 'hat')
0.25
>>> sim_ncd_bwtrle('Niall', 'Neil')
0.16666666666666663
>>> sim_ncd_bwtrle('aluminum', 'Catalan')
0.0
>>> sim_ncd_bwtrle('ATCG', 'TAGC')
0.19999999999999996

New in version 0.3.5.

class abydos.distance.NCDrle(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using RLE.

Cf. https://en.wikipedia.org/wiki/Run-length_encoding

Normalized compression distance (NCD) [CV05].

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the NCD between two strings using RLE.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> cmp = NCDrle()
>>> cmp.dist('cat', 'hat')
1.0
>>> cmp.dist('Niall', 'Neil')
1.0
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.3.5.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_ncd_rle(src, tar)[source]

Return the NCD between two strings using RLE.

This is a wrapper for NCDrle.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Examples

>>> dist_ncd_rle('cat', 'hat')
1.0
>>> dist_ncd_rle('Niall', 'Neil')
1.0
>>> dist_ncd_rle('aluminum', 'Catalan')
1.0
>>> dist_ncd_rle('ATCG', 'TAGC')
1.0

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDrle.dist method instead.

abydos.distance.sim_ncd_rle(src, tar)[source]

Return the NCD similarity between two strings using RLE.

This is a wrapper for NCDrle.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression similarity

Return type

float

Examples

>>> sim_ncd_rle('cat', 'hat')
0.0
>>> sim_ncd_rle('Niall', 'Neil')
0.0
>>> sim_ncd_rle('aluminum', 'Catalan')
0.0
>>> sim_ncd_rle('ATCG', 'TAGC')
0.0

New in version 0.3.5.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the NCDrle.sim method instead.

class abydos.distance.NCDpaq9a(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using PAQ9A compression.

Cf. http://mattmahoney.net/dc/#paq9a

Normalized compression distance (NCD) [CV05].

New in version 0.4.0.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the NCD between two strings using PAQ9A compression.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Raises

ValueError -- Install the paq module in order to use PAQ9A

Examples

>>> cmp = NCDpaq9a()
>>> cmp.dist('cat', 'hat')
0.42857142857142855
>>> cmp.dist('Niall', 'Neil')
0.5555555555555556
>>> cmp.dist('aluminum', 'Catalan')
0.5833333333333334
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.4.0.

class abydos.distance.NCDlzss(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Normalized Compression Distance using LZSS compression.

Cf. https://en.wikipedia.org/wiki/Lempel-Ziv-Storer-Szymanski

Normalized compression distance (NCD) [CV05].

New in version 0.4.0.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the NCD between two strings using LZSS compression.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Compression distance

Return type

float

Raises

ValueError -- Install the PyLZSS module in order to use LZSS

Examples

>>> cmp = NCDlzss()
>>> cmp.dist('cat', 'hat')
0.75
>>> cmp.dist('Niall', 'Neil')
1.0
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
0.8

New in version 0.4.0.

class abydos.distance.FuzzyWuzzyPartialString(**kwargs)[source]

Bases: abydos.distance._distance._Distance

FuzzyWuzzy Partial String similarity.

This follows the FuzzyWuzzy Partial String similarity algorithm [Coh11]. Rather than returning an integer in the range [0, 100], as demonstrated in the blog post, this implementation returns a float in the range [0.0, 1.0].

New in version 0.4.0.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the FuzzyWuzzy Partial String similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

FuzzyWuzzy Partial String similarity

Return type

float

Examples

>>> cmp = FuzzyWuzzyPartialString()
>>> round(cmp.sim('cat', 'hat'), 12)
0.666666666667
>>> round(cmp.sim('Niall', 'Neil'), 12)
0.75
>>> round(cmp.sim('aluminum', 'Catalan'), 12)
0.428571428571
>>> cmp.sim('ATCG', 'TAGC')
0.5

New in version 0.4.0.

class abydos.distance.FuzzyWuzzyTokenSort(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

FuzzyWuzzy Token Sort similarity.

This follows the FuzzyWuzzy Token Sort similarity algorithm [Coh11]. Rather than returning an integer in the range [0, 100], as demonstrated in the blog post, this implementation returns a float in the range [0.0, 1.0].

New in version 0.4.0.

Initialize FuzzyWuzzyTokenSort instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package. By default, the regexp tokenizer is employed, matching only letters.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the FuzzyWuzzy Token Sort similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

FuzzyWuzzy Token Sort similarity

Return type

float

Examples

>>> cmp = FuzzyWuzzyTokenSort()
>>> cmp.sim('cat', 'hat')
0.6666666666666666
>>> cmp.sim('Niall', 'Neil')
0.6666666666666666
>>> cmp.sim('aluminum', 'Catalan')
0.4
>>> cmp.sim('ATCG', 'TAGC')
0.5

New in version 0.4.0.

class abydos.distance.FuzzyWuzzyTokenSet(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

FuzzyWuzzy Token Set similarity.

This follows the FuzzyWuzzy Token Set similarity algorithm [Coh11]. Rather than returning an integer in the range [0, 100], as demonstrated in the blog post, this implementation returns a float in the range [0.0, 1.0]. Distinct from the

New in version 0.4.0.

Initialize FuzzyWuzzyTokenSet instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package. By default, the regexp tokenizer is employed, matching only letters.

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.0.

sim(src, tar)[source]

Return the FuzzyWuzzy Token Set similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

FuzzyWuzzy Token Set similarity

Return type

float

Examples

>>> cmp = FuzzyWuzzyTokenSet()
>>> cmp.sim('cat', 'hat')
0.75
>>> cmp.sim('Niall', 'Neil')
0.7272727272727273
>>> cmp.sim('aluminum', 'Catalan')
0.47058823529411764
>>> cmp.sim('ATCG', 'TAGC')
0.6

New in version 0.4.0.

class abydos.distance.PhoneticDistance(transforms=None, metric=None, encode_alpha=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Phonetic distance.

Phonetic distance applies one or more supplied string transformations to words and compares the resulting transformed strings using a supplied distance measure.

A simple example would be to create a 'Soundex distance':

>>> from abydos.phonetic import Soundex
>>> soundex = PhoneticDistance(transforms=Soundex())
>>> soundex.dist('Ashcraft', 'Ashcroft')
0.0
>>> soundex.dist('Robert', 'Ashcraft')
1.0

New in version 0.4.1.

Initialize PhoneticDistance instance.

Parameters
  • transforms (list or _Phonetic or _Stemmer or _Fingerprint or type) -- An instance of a subclass of _Phonetic, _Stemmer, or _Fingerprint, or a list (or other iterable) of such instances to apply to each input word before computing their distance or similarity. If omitted, no transformations will be performed.

  • metric (_Distance or type) -- An instance of a subclass of _Distance, used for computing the inputs' distance or similarity after being transformed. If omitted, the strings will be compared for identify (returning 0.0 if identical, otherwise 1.0, when distance is computed).

  • encode_alpha (bool) -- Set to true to use the encode_alpha method of phonetic algoritms whenever possible.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

dist(src, tar)[source]

Return the normalized Phonetic distance.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Phonetic distance

Return type

float

Examples

>>> from abydos.phonetic import Soundex
>>> cmp = PhoneticDistance(Soundex())
>>> cmp.dist('cat', 'hat')
1.0
>>> cmp.dist('Niall', 'Neil')
0.0
>>> cmp.dist('Colin', 'Cuilen')
0.0
>>> cmp.dist('ATCG', 'TAGC')
1.0
>>> from abydos.distance import Levenshtein
>>> cmp = PhoneticDistance(transforms=[Soundex], metric=Levenshtein)
>>> cmp.dist('cat', 'hat')
0.25
>>> cmp.dist('Niall', 'Neil')
0.0
>>> cmp.dist('Colin', 'Cuilen')
0.0
>>> cmp.dist('ATCG', 'TAGC')
0.75

New in version 0.4.1.

dist_abs(src, tar)[source]

Return the Phonetic distance.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Phonetic distance

Return type

float or int

Examples

>>> from abydos.phonetic import Soundex
>>> cmp = PhoneticDistance(Soundex())
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
0
>>> cmp.dist_abs('Colin', 'Cuilen')
0
>>> cmp.dist_abs('ATCG', 'TAGC')
1
>>> from abydos.distance import Levenshtein
>>> cmp = PhoneticDistance(transforms=[Soundex], metric=Levenshtein)
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
0
>>> cmp.dist_abs('Colin', 'Cuilen')
0
>>> cmp.dist_abs('ATCG', 'TAGC')
3

New in version 0.4.1.

class abydos.distance.MRA(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Match Rating Algorithm comparison rating.

The Western Airlines Surname Match Rating Algorithm comparison rating, as presented on page 18 of [MKTM77].

New in version 0.3.6.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the MRA comparison rating of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

MRA comparison rating

Return type

int

Examples

>>> cmp = MRA()
>>> cmp.dist_abs('cat', 'hat')
5
>>> cmp.dist_abs('Niall', 'Neil')
6
>>> cmp.dist_abs('aluminum', 'Catalan')
0
>>> cmp.dist_abs('ATCG', 'TAGC')
5

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

sim(src, tar)[source]

Return the normalized MRA similarity of two strings.

This is the MRA normalized to \([0, 1]\), given that MRA itself is constrained to the range \([0, 6]\).

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized MRA similarity

Return type

float

Examples

>>> cmp = MRA()
>>> cmp.sim('cat', 'hat')
0.8333333333333334
>>> cmp.sim('Niall', 'Neil')
1.0
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.8333333333333334

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.mra_compare(src, tar)[source]

Return the MRA comparison rating of two strings.

This is a wrapper for MRA.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

MRA comparison rating

Return type

int

Examples

>>> mra_compare('cat', 'hat')
5
>>> mra_compare('Niall', 'Neil')
6
>>> mra_compare('aluminum', 'Catalan')
0
>>> mra_compare('ATCG', 'TAGC')
5

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MRA.dist_abs method instead.

abydos.distance.dist_mra(src, tar)[source]

Return the normalized MRA distance between two strings.

This is a wrapper for MRA.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized MRA distance

Return type

float

Examples

>>> dist_mra('cat', 'hat')
0.16666666666666663
>>> dist_mra('Niall', 'Neil')
0.0
>>> dist_mra('aluminum', 'Catalan')
1.0
>>> dist_mra('ATCG', 'TAGC')
0.16666666666666663

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MRA.dist method instead.

abydos.distance.sim_mra(src, tar)[source]

Return the normalized MRA similarity of two strings.

This is a wrapper for MRA.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized MRA similarity

Return type

float

Examples

>>> sim_mra('cat', 'hat')
0.8333333333333334
>>> sim_mra('Niall', 'Neil')
1.0
>>> sim_mra('aluminum', 'Catalan')
0.0
>>> sim_mra('ATCG', 'TAGC')
0.8333333333333334

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the MRA.sim method instead.

class abydos.distance.Editex(cost=(0, 1, 2), local=False, taper=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Editex.

As described on pages 3 & 4 of [ZD96].

The local variant is based on [RU09].

New in version 0.3.6.

Changed in version 0.4.0: Added taper option

Initialize Editex instance.

Parameters
  • cost (tuple) -- A 3-tuple representing the cost of the four possible edits: match, same-group, and mismatch respectively (by default: (0, 1, 2))

  • local (bool) -- If True, the local variant of Editex is used

  • taper (bool) -- Enables cost tapering. Following [ZD96], it causes edits at the start of the string to "just [exceed] twice the minimum penalty for replacement or deletion at the end of the string".

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Editex distance between two strings.

The Editex distance is normalized by dividing the Editex distance (calculated by any of the three supported methods) by the greater of the number of characters in src times the cost of a delete and the number of characters in tar times the cost of an insert. For the case in which all operations have \(cost = 1\), this is equivalent to the greater of the length of the two strings src & tar.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Editex distance

Return type

int

Examples

>>> cmp = Editex()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.2
>>> cmp.dist('aluminum', 'Catalan')
0.75
>>> cmp.dist('ATCG', 'TAGC')
0.75

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the Editex distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Editex distance

Return type

int

Examples

>>> cmp = Editex()
>>> cmp.dist_abs('cat', 'hat')
2
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('aluminum', 'Catalan')
12
>>> cmp.dist_abs('ATCG', 'TAGC')
6

New in version 0.1.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.editex(src, tar, cost=(0, 1, 2), local=False)[source]

Return the Editex distance between two strings.

This is a wrapper for Editex.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • cost (tuple) -- A 3-tuple representing the cost of the four possible edits: match, same-group, and mismatch respectively (by default: (0, 1, 2))

  • local (bool) -- If True, the local variant of Editex is used

Returns

Editex distance

Return type

int

Examples

>>> editex('cat', 'hat')
2
>>> editex('Niall', 'Neil')
2
>>> editex('aluminum', 'Catalan')
12
>>> editex('ATCG', 'TAGC')
6

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Editex.dist_abs method instead.

abydos.distance.dist_editex(src, tar, cost=(0, 1, 2), local=False)[source]

Return the normalized Editex distance between two strings.

This is a wrapper for Editex.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • cost (tuple) -- A 3-tuple representing the cost of the four possible edits: match, same-group, and mismatch respectively (by default: (0, 1, 2))

  • local (bool) -- If True, the local variant of Editex is used

Returns

Normalized Editex distance

Return type

int

Examples

>>> round(dist_editex('cat', 'hat'), 12)
0.333333333333
>>> round(dist_editex('Niall', 'Neil'), 12)
0.2
>>> dist_editex('aluminum', 'Catalan')
0.75
>>> dist_editex('ATCG', 'TAGC')
0.75

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Editex.dist method instead.

abydos.distance.sim_editex(src, tar, cost=(0, 1, 2), local=False)[source]

Return the normalized Editex similarity of two strings.

This is a wrapper for Editex.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • cost (tuple) -- A 3-tuple representing the cost of the four possible edits: match, same-group, and mismatch respectively (by default: (0, 1, 2))

  • local (bool) -- If True, the local variant of Editex is used

Returns

Normalized Editex similarity

Return type

int

Examples

>>> round(sim_editex('cat', 'hat'), 12)
0.666666666667
>>> round(sim_editex('Niall', 'Neil'), 12)
0.8
>>> sim_editex('aluminum', 'Catalan')
0.25
>>> sim_editex('ATCG', 'TAGC')
0.25

New in version 0.1.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Editex.sim method instead.

class abydos.distance.Baystat(min_ss_len=None, left_ext=None, right_ext=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Baystat similarity and distance.

Good results for shorter words are reported when setting min_ss_len to 1 and either left_ext OR right_ext to 1.

The Baystat similarity is defined in [FurnrohrRvR02].

This is ostensibly a port of the R module PPRL's implementation: https://github.com/cran/PPRL/blob/master/src/MTB_Baystat.cpp [Ruk18]. As such, this could be made more pythonic.

New in version 0.3.6.

Initialize Levenshtein instance.

Parameters
  • min_ss_len (int) -- Minimum substring length to be considered

  • left_ext (int) -- Left-side extension length

  • right_ext (int) -- Right-side extension length

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the Baystat similarity.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Baystat similarity

Return type

float

Examples

>>> cmp = Baystat()
>>> round(cmp.sim('cat', 'hat'), 12)
0.666666666667
>>> cmp.sim('Niall', 'Neil')
0.4
>>> round(cmp.sim('Colin', 'Cuilen'), 12)
0.166666666667
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.dist_baystat(src, tar, min_ss_len=None, left_ext=None, right_ext=None)[source]

Return the Baystat distance.

This is a wrapper for Baystat.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • min_ss_len (int) -- Minimum substring length to be considered

  • left_ext (int) -- Left-side extension length

  • right_ext (int) -- Right-side extension length

Returns

The Baystat distance

Return type

float

Examples

>>> round(dist_baystat('cat', 'hat'), 12)
0.333333333333
>>> dist_baystat('Niall', 'Neil')
0.6
>>> round(dist_baystat('Colin', 'Cuilen'), 12)
0.833333333333
>>> dist_baystat('ATCG', 'TAGC')
1.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Baystat.dist method instead.

abydos.distance.sim_baystat(src, tar, min_ss_len=None, left_ext=None, right_ext=None)[source]

Return the Baystat similarity.

This is a wrapper for Baystat.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • min_ss_len (int) -- Minimum substring length to be considered

  • left_ext (int) -- Left-side extension length

  • right_ext (int) -- Right-side extension length

Returns

The Baystat similarity

Return type

float

Examples

>>> round(sim_baystat('cat', 'hat'), 12)
0.666666666667
>>> sim_baystat('Niall', 'Neil')
0.4
>>> round(sim_baystat('Colin', 'Cuilen'), 12)
0.166666666667
>>> sim_baystat('ATCG', 'TAGC')
0.0

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Baystat.sim method instead.

class abydos.distance.Eudex(weights='exponential', max_length=8, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Distance between the Eudex hashes of two terms.

Cf. [Tic].

New in version 0.3.6.

Initialize Eudex instance.

Parameters
  • weights (str, iterable, or generator function) --

    The weights or weights generator function

    • If set to None, a simple Hamming distance is calculated.

    • If set to exponential, weight decays by powers of 2, as proposed in the eudex specification: https://github.com/ticki/eudex.

    • If set to fibonacci, weight decays through the Fibonacci series, as in the eudex reference implementation.

    • If set to a callable function, this assumes it creates a generator and the generator is used to populate a series of weights.

    • If set to an iterable, the iterable's values should be integers and will be used as the weights.

    In all cases, the weights should be ordered or generated from least significant to most significant, so larger values should generally come first.

  • max_length (int) -- The number of characters to encode as a eudex hash

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return normalized distance between the Eudex hashes of two terms.

This is Eudex distance normalized to [0, 1].

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Eudex Hamming distance

Return type

int

Examples

>>> cmp = Eudex()
>>> round(cmp.dist('cat', 'hat'), 12)
0.062745098039
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.000980392157
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.004901960784
>>> round(cmp.dist('ATCG', 'TAGC'), 12)
0.197549019608

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar, normalized=False)[source]

Calculate the distance between the Eudex hashes of two terms.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • normalized (bool) -- Normalizes to [0, 1] if True

Returns

The Eudex Hamming distance

Return type

int

Examples

>>> cmp = Eudex()
>>> cmp.dist_abs('cat', 'hat')
128
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('Colin', 'Cuilen')
10
>>> cmp.dist_abs('ATCG', 'TAGC')
403
>>> cmp = Eudex(weights='fibonacci')
>>> cmp.dist_abs('cat', 'hat')
34
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('Colin', 'Cuilen')
7
>>> cmp.dist_abs('ATCG', 'TAGC')
117
>>> cmp = Eudex(weights=None)
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
1
>>> cmp.dist_abs('Colin', 'Cuilen')
2
>>> cmp.dist_abs('ATCG', 'TAGC')
9
>>> # Using the OEIS A000142:
>>> cmp = Eudex(weights=[1, 1, 2, 6, 24, 120, 720, 5040])
>>> cmp.dist_abs('cat', 'hat')
5040
>>> cmp.dist_abs('Niall', 'Neil')
1
>>> cmp.dist_abs('Colin', 'Cuilen')
7
>>> cmp.dist_abs('ATCG', 'TAGC')
15130

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

static gen_exponential(base=2)[source]

Yield the next value in an exponential series of the base.

Starts at base**0

Parameters

base (int) -- The base to exponentiate

Yields

int -- The next power of base

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

static gen_fibonacci()[source]

Yield the next Fibonacci number.

Based on https://www.python-course.eu/generators.php Starts at Fibonacci number 3 (the second 1)

Yields

int -- The next Fibonacci number

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.eudex_hamming(src, tar, weights='exponential', max_length=8, normalized=False)[source]

Calculate the Hamming distance between the Eudex hashes of two terms.

This is a wrapper for Eudex.eudex_hamming().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • weights (str, iterable, or generator function) -- The weights or weights generator function

  • max_length (int) -- The number of characters to encode as a eudex hash

  • normalized (bool) -- Normalizes to [0, 1] if True

Returns

The Eudex Hamming distance

Return type

int

Examples

>>> eudex_hamming('cat', 'hat')
128
>>> eudex_hamming('Niall', 'Neil')
2
>>> eudex_hamming('Colin', 'Cuilen')
10
>>> eudex_hamming('ATCG', 'TAGC')
403
>>> eudex_hamming('cat', 'hat', weights='fibonacci')
34
>>> eudex_hamming('Niall', 'Neil', weights='fibonacci')
2
>>> eudex_hamming('Colin', 'Cuilen', weights='fibonacci')
7
>>> eudex_hamming('ATCG', 'TAGC', weights='fibonacci')
117
>>> eudex_hamming('cat', 'hat', weights=None)
1
>>> eudex_hamming('Niall', 'Neil', weights=None)
1
>>> eudex_hamming('Colin', 'Cuilen', weights=None)
2
>>> eudex_hamming('ATCG', 'TAGC', weights=None)
9
>>> # Using the OEIS A000142:
>>> eudex_hamming('cat', 'hat', [1, 1, 2, 6, 24, 120, 720, 5040])
5040
>>> eudex_hamming('Niall', 'Neil', [1, 1, 2, 6, 24, 120, 720, 5040])
1
>>> eudex_hamming('Colin', 'Cuilen', [1, 1, 2, 6, 24, 120, 720, 5040])
7
>>> eudex_hamming('ATCG', 'TAGC', [1, 1, 2, 6, 24, 120, 720, 5040])
15130

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Eudex.dist_abs method instead.

abydos.distance.dist_eudex(src, tar, weights='exponential', max_length=8)[source]

Return normalized Hamming distance between Eudex hashes of two terms.

This is a wrapper for Eudex.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • weights (str, iterable, or generator function) -- The weights or weights generator function

  • max_length (int) -- The number of characters to encode as a eudex hash

Returns

The normalized Eudex Hamming distance

Return type

int

Examples

>>> round(dist_eudex('cat', 'hat'), 12)
0.062745098039
>>> round(dist_eudex('Niall', 'Neil'), 12)
0.000980392157
>>> round(dist_eudex('Colin', 'Cuilen'), 12)
0.004901960784
>>> round(dist_eudex('ATCG', 'TAGC'), 12)
0.197549019608

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Eudex.dist method instead.

abydos.distance.sim_eudex(src, tar, weights='exponential', max_length=8)[source]

Return normalized Hamming similarity between Eudex hashes of two terms.

This is a wrapper for Eudex.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • weights (str, iterable, or generator function) -- The weights or weights generator function

  • max_length (int) -- The number of characters to encode as a eudex hash

Returns

The normalized Eudex Hamming similarity

Return type

int

Examples

>>> round(sim_eudex('cat', 'hat'), 12)
0.937254901961
>>> round(sim_eudex('Niall', 'Neil'), 12)
0.999019607843
>>> round(sim_eudex('Colin', 'Cuilen'), 12)
0.995098039216
>>> round(sim_eudex('ATCG', 'TAGC'), 12)
0.802450980392

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Eudex.sim method instead.

class abydos.distance.Sift4(max_offset=5, max_distance=0, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Sift4 Common version.

This is an approximation of edit distance, described in [Zac14].

New in version 0.3.6.

Initialize Sift4 instance.

Parameters
  • max_offset (int) -- The number of characters to search for matching letters

  • max_distance (int) -- The distance at which to stop and exit

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized "common" Sift4 distance between two terms.

This is Sift4 distance, normalized to [0, 1].

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The normalized Sift4 distance

Return type

float

Examples

>>> cmp = Sift4()
>>> round(cmp.dist('cat', 'hat'), 12)
0.333333333333
>>> cmp.dist('Niall', 'Neil')
0.4
>>> cmp.dist('Colin', 'Cuilen')
0.5
>>> cmp.dist('ATCG', 'TAGC')
0.5

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the "common" Sift4 distance between two terms.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Sift4 distance according to the common formula

Return type

int

Examples

>>> cmp = Sift4()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('Colin', 'Cuilen')
3
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

class abydos.distance.Sift4Simplest(max_offset=5, **kwargs)[source]

Bases: abydos.distance._sift4.Sift4

Sift4 Simplest version.

This is an approximation of edit distance, described in [Zac14].

New in version 0.3.6.

Initialize Sift4Simplest instance.

Parameters
  • max_offset (int) -- The number of characters to search for matching letters

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the "simplest" Sift4 distance between two terms.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Sift4 distance according to the simplest formula

Return type

int

Examples

>>> cmp = Sift4Simplest()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('Colin', 'Cuilen')
3
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

class abydos.distance.Sift4Extended(max_offset=5, max_distance=0, tokenizer=None, token_matcher=None, matching_evaluator=None, local_length_evaluator=None, transposition_cost_evaluator=None, transpositions_evaluator=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Sift4 Extended version.

This is an approximation of edit distance, described in [Zac14].

New in version 0.4.0.

Initialize Sift4Extended instance.

Parameters
  • max_offset (int) -- The number of characters to search for matching letters

  • max_distance (int) -- The distance at which to stop and exit

  • tokenizer (_Tokenizer) -- A tokenizer instance (character tokenization by default)

  • token_matcher (function) -- A token matcher function of two parameters (equality by default). \(Sift4Extended.sift4_token_matcher\) is also supplied.

  • matching_evaluator (function) -- A token match quality function of two parameters (1 by default). \(Sift4Extended.sift4_matching_evaluator\) is also supplied.

  • local_length_evaluator (function) -- A local length evaluator function (its single parameter by default). \(Sift4Extended.reward_length_evaluator\) and \(Sift4Extended.reward_length_evaluator_exp\) are also supplied.

  • transposition_cost_evaluator (function) -- A transposition cost evaluator function of two parameters (1 by default). \(Sift4Extended.longer_transpositions_are_more_costly\) is also supplied.

  • transpositions_evaluator (function) -- A transpositions evaluator function of two parameters (the second parameter subtracted from the first, by default).

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Sift4 Extended distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The Sift4 distance according to the extended formula

Return type

int

Examples

>>> cmp = Sift4Extended()
>>> cmp.dist_abs('cat', 'hat')
1
>>> cmp.dist_abs('Niall', 'Neil')
2
>>> cmp.dist_abs('aluminum', 'Catalan')
5
>>> cmp.dist_abs('ATCG', 'TAGC')
2

New in version 0.4.0.

static longer_transpositions_are_more_costly(pos1, pos2)[source]

Longer Transpositions Are More Costly.

Parameters
  • pos1 (int) -- The position of the first transposition

  • pos2 (int) -- The position of the second transposition

Returns

  • float -- A cost that grows as difference in the positions increases

  • .. versionadded:: 0.4.0

static reward_length_evaluator(length)[source]

Reward Length Evaluator.

Parameters

length (int) -- The length of a local match

Returns

  • float -- A reward value that grows sub-linearly

  • .. versionadded:: 0.4.0

static reward_length_evaluator_exp(length)[source]

Reward Length Evaluator.

Parameters

length (int) -- The length of a local match

Returns

  • float -- A reward value that grows exponentially

  • .. versionadded:: 0.4.0

static sift4_matching_evaluator(src, tar)[source]

Sift4 Matching Evaluator.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

  • float -- The Sift4 similarity of the two tokens

  • .. versionadded:: 0.4.0

static sift4_token_matcher(src, tar)[source]

Sift4 Token Matcher.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

  • bool -- Whether the Sift4 similarity of the two tokens is over 0.7

  • .. versionadded:: 0.4.0

abydos.distance.sift4_common(src, tar, max_offset=5, max_distance=0)[source]

Return the "common" Sift4 distance between two terms.

This is a wrapper for Sift4.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • max_offset (int) -- The number of characters to search for matching letters

  • max_distance (int) -- The distance at which to stop and exit

Returns

The Sift4 distance according to the common formula

Return type

int

Examples

>>> sift4_common('cat', 'hat')
1
>>> sift4_common('Niall', 'Neil')
2
>>> sift4_common('Colin', 'Cuilen')
3
>>> sift4_common('ATCG', 'TAGC')
2

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Sift4.dist_abs method instead.

abydos.distance.sift4_simplest(src, tar, max_offset=5)[source]

Return the "simplest" Sift4 distance between two terms.

This is a wrapper for Sift4Simplest.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • max_offset (int) -- The number of characters to search for matching letters

Returns

The Sift4 distance according to the simplest formula

Return type

int

Examples

>>> sift4_simplest('cat', 'hat')
1
>>> sift4_simplest('Niall', 'Neil')
2
>>> sift4_simplest('Colin', 'Cuilen')
3
>>> sift4_simplest('ATCG', 'TAGC')
2

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Sift4Simplest.dist_abs method instead.

abydos.distance.dist_sift4(src, tar, max_offset=5, max_distance=0)[source]

Return the normalized "common" Sift4 distance between two terms.

This is a wrapper for Sift4.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • max_offset (int) -- The number of characters to search for matching letters

  • max_distance (int) -- The distance at which to stop and exit

Returns

The normalized Sift4 distance

Return type

float

Examples

>>> round(dist_sift4('cat', 'hat'), 12)
0.333333333333
>>> dist_sift4('Niall', 'Neil')
0.4
>>> dist_sift4('Colin', 'Cuilen')
0.5
>>> dist_sift4('ATCG', 'TAGC')
0.5

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Sift4.dist method instead.

abydos.distance.sim_sift4(src, tar, max_offset=5, max_distance=0)[source]

Return the normalized "common" Sift4 similarity of two terms.

This is a wrapper for Sift4.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • max_offset (int) -- The number of characters to search for matching letters

  • max_distance (int) -- The distance at which to stop and exit

Returns

The normalized Sift4 similarity

Return type

float

Examples

>>> round(sim_sift4('cat', 'hat'), 12)
0.666666666667
>>> sim_sift4('Niall', 'Neil')
0.6
>>> sim_sift4('Colin', 'Cuilen')
0.5
>>> sim_sift4('ATCG', 'TAGC')
0.5

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Sift4.sim method instead.

class abydos.distance.Typo(metric='euclidean', cost=(1, 1, 0.5, 0.5), layout='QWERTY', failsafe=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Typo distance.

This is inspired by Typo-Distance [Son11], and a fair bit of this was copied from that module. Compared to the original, this supports different metrics for substitution.

New in version 0.3.6.

Initialize Typo instance.

Parameters
  • metric (str) -- Supported values include: euclidean, manhattan, log-euclidean, and log-manhattan

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and shift, respectively (by default: (1, 1, 0.5, 0.5)) The substitution & shift costs should be significantly less than the cost of an insertion & deletion unless a log metric is used.

  • layout (str) -- Name of the keyboard layout to use (Currently supported: QWERTY, Dvorak, AZERTY, QWERTZ, auto). If auto is selected, the class will attempt to determine an appropriate keyboard based on the supplied words.

  • failsafe (bool) -- If True, substitution of an unknown character (one not present on the selected keyboard) will incur a cost equal to an insertion plus a deletion.

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized typo distance between two strings.

This is typo distance, normalized to [0, 1].

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized typo distance

Return type

float

Examples

>>> cmp = Typo()
>>> round(cmp.dist('cat', 'hat'), 12)
0.527046283086
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.565028142929
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.569035609563
>>> cmp.dist('ATCG', 'TAGC')
0.625

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar)[source]

Return the typo distance between two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Typo distance

Return type

float

Raises

ValueError -- char not found in any keyboard layouts

Examples

>>> cmp = Typo()
>>> cmp.dist_abs('cat', 'hat')
1.5811388
>>> cmp.dist_abs('Niall', 'Neil')
2.8251407
>>> cmp.dist_abs('Colin', 'Cuilen')
3.4142137
>>> cmp.dist_abs('ATCG', 'TAGC')
2.5
>>> cmp = Typo(metric='manhattan')
>>> cmp.dist_abs('cat', 'hat')
2.0
>>> cmp.dist_abs('Niall', 'Neil')
3.0
>>> cmp.dist_abs('Colin', 'Cuilen')
3.5
>>> cmp.dist_abs('ATCG', 'TAGC')
2.5
>>> cmp = Typo(metric='log-manhattan')
>>> cmp.dist_abs('cat', 'hat')
0.804719
>>> cmp.dist_abs('Niall', 'Neil')
2.2424533
>>> cmp.dist_abs('Colin', 'Cuilen')
2.2424533
>>> cmp.dist_abs('ATCG', 'TAGC')
2.3465736

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.typo(src, tar, metric='euclidean', cost=(1, 1, 0.5, 0.5), layout='QWERTY')[source]

Return the typo distance between two strings.

This is a wrapper for Typo.typo().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • metric (str) -- Supported values include: euclidean, manhattan, log-euclidean, and log-manhattan

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and shift, respectively (by default: (1, 1, 0.5, 0.5)) The substitution & shift costs should be significantly less than the cost of an insertion & deletion unless a log metric is used.

  • layout (str) -- Name of the keyboard layout to use (Currently supported: QWERTY, Dvorak, AZERTY, QWERTZ)

Returns

Typo distance

Return type

float

Examples

>>> typo('cat', 'hat')
1.5811388
>>> typo('Niall', 'Neil')
2.8251407
>>> typo('Colin', 'Cuilen')
3.4142137
>>> typo('ATCG', 'TAGC')
2.5
>>> typo('cat', 'hat', metric='manhattan')
2.0
>>> typo('Niall', 'Neil', metric='manhattan')
3.0
>>> typo('Colin', 'Cuilen', metric='manhattan')
3.5
>>> typo('ATCG', 'TAGC', metric='manhattan')
2.5
>>> typo('cat', 'hat', metric='log-manhattan')
0.804719
>>> typo('Niall', 'Neil', metric='log-manhattan')
2.2424533
>>> typo('Colin', 'Cuilen', metric='log-manhattan')
2.2424533
>>> typo('ATCG', 'TAGC', metric='log-manhattan')
2.3465736

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Typo.dist_abs method instead.

abydos.distance.dist_typo(src, tar, metric='euclidean', cost=(1, 1, 0.5, 0.5), layout='QWERTY')[source]

Return the normalized typo distance between two strings.

This is a wrapper for Typo.dist().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • metric (str) -- Supported values include: euclidean, manhattan, log-euclidean, and log-manhattan

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and shift, respectively (by default: (1, 1, 0.5, 0.5)) The substitution & shift costs should be significantly less than the cost of an insertion & deletion unless a log metric is used.

  • layout (str) -- Name of the keyboard layout to use (Currently supported: QWERTY, Dvorak, AZERTY, QWERTZ)

Returns

Normalized typo distance

Return type

float

Examples

>>> round(dist_typo('cat', 'hat'), 12)
0.527046283086
>>> round(dist_typo('Niall', 'Neil'), 12)
0.565028142929
>>> round(dist_typo('Colin', 'Cuilen'), 12)
0.569035609563
>>> dist_typo('ATCG', 'TAGC')
0.625

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Typo.dist method instead.

abydos.distance.sim_typo(src, tar, metric='euclidean', cost=(1, 1, 0.5, 0.5), layout='QWERTY')[source]

Return the normalized typo similarity between two strings.

This is a wrapper for Typo.sim().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • metric (str) -- Supported values include: euclidean, manhattan, log-euclidean, and log-manhattan

  • cost (tuple) -- A 4-tuple representing the cost of the four possible edits: inserts, deletes, substitutions, and shift, respectively (by default: (1, 1, 0.5, 0.5)) The substitution & shift costs should be significantly less than the cost of an insertion & deletion unless a log metric is used.

  • layout (str) -- Name of the keyboard layout to use (Currently supported: QWERTY, Dvorak, AZERTY, QWERTZ)

Returns

Normalized typo similarity

Return type

float

Examples

>>> round(sim_typo('cat', 'hat'), 12)
0.472953716914
>>> round(sim_typo('Niall', 'Neil'), 12)
0.434971857071
>>> round(sim_typo('Colin', 'Cuilen'), 12)
0.430964390437
>>> sim_typo('ATCG', 'TAGC')
0.375

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Typo.sim method instead.

class abydos.distance.Synoname(word_approx_min=0.3, char_approx_min=0.73, tests=4095, ret_name=False, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Synoname.

Cf. [JPGTrust91][Gro91]

New in version 0.3.6.

Initialize Synoname instance.

Parameters
  • word_approx_min (float) -- The minimum word approximation value to signal a 'word_approx' match

  • char_approx_min (float) -- The minimum character approximation value to signal a 'char_approx' match

  • tests (int or Iterable) -- Either an integer indicating tests to perform or a list of test names to perform (defaults to performing all tests)

  • ret_name (bool) -- If True, returns the match name rather than its integer equivalent

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Synoname distance between two words.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Synoname distance

Return type

float

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

dist_abs(src, tar, force_numeric=False)[source]

Return the Synoname similarity type of two words.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • force_numeric (bool) -- Overrides the instance's ret_name setting

Returns

Synoname value

Return type

int (or str if ret_name is True)

Examples

>>> cmp = Synoname()
>>> cmp.dist_abs(('Breghel', 'Pieter', ''), ('Brueghel', 'Pieter', ''))
2
>>> cmp = Synoname(ret_name=True)
>>> cmp.dist_abs(('Breghel', 'Pieter', ''), ('Brueghel', 'Pieter', ''))
'omission'
>>> cmp.dist_abs(('Dore', 'Gustave', ''),
... ('Dore', 'Paul Gustave Louis Christophe', ''))
'inclusion'
>>> cmp.dist_abs(('Pereira', 'I. R.', ''), ('Pereira', 'I. Smith', ''))
'word_approx'

New in version 0.3.0.

Changed in version 0.3.6: Encapsulated in class

abydos.distance.synoname(src, tar, word_approx_min=0.3, char_approx_min=0.73, tests=4095, ret_name=False)[source]

Return the Synoname similarity type of two words.

This is a wrapper for Synoname.dist_abs().

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

  • word_approx_min (float) -- The minimum word approximation value to signal a 'word_approx' match

  • char_approx_min (float) -- The minimum character approximation value to signal a 'char_approx' match

  • tests (int or Iterable) -- Either an integer indicating tests to perform or a list of test names to perform (defaults to performing all tests)

  • ret_name (bool) -- If True, returns the match name rather than its integer equivalent

Returns

Synoname value

Return type

int (or str if ret_name is True)

Examples

>>> synoname(('Breghel', 'Pieter', ''), ('Brueghel', 'Pieter', ''))
2
>>> synoname(('Breghel', 'Pieter', ''), ('Brueghel', 'Pieter', ''),
... ret_name=True)
'omission'
>>> synoname(('Dore', 'Gustave', ''),
... ('Dore', 'Paul Gustave Louis Christophe', ''), ret_name=True)
'inclusion'
>>> synoname(('Pereira', 'I. R.', ''), ('Pereira', 'I. Smith', ''),
... ret_name=True)
'word_approx'

New in version 0.3.0.

Deprecated since version 0.4.0: This will be removed in 0.6.0. Use the Synoname.dist_abs method instead.

class abydos.distance.Ozbay(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Ozbay metric.

The Ozbay metric [Ozb15] is a string distance measure developed by Hakan Ozbay, which combines Jaccard distance, Levenshtein distance, and longest common substring distance.

The normalized variant should be considered experimental.

New in version 0.4.0.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the normalized Ozbay distance.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Normalized Ozbay distance

Return type

float

Examples

>>> cmp = Ozbay()
>>> round(cmp.dist('cat', 'hat'), 12)
0.027777777778
>>> round(cmp.dist('Niall', 'Neil'), 12)
0.24
>>> round(cmp.dist('Colin', 'Cuilen'), 12)
0.214285714286
>>> cmp.dist('ATCG', 'TAGC')
0.140625

New in version 0.4.0.

dist_abs(src, tar)[source]

Return the Ozbay metric.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Ozbay metric

Return type

float

Examples

>>> cmp = Ozbay()
>>> round(cmp.dist_abs('cat', 'hat'), 12)
0.75
>>> round(cmp.dist_abs('Niall', 'Neil'), 12)
6.0
>>> round(cmp.dist_abs('Colin', 'Cuilen'), 12)
7.714285714286
>>> cmp.dist_abs('ATCG', 'TAGC')
3.0

New in version 0.4.0.

class abydos.distance.ISG(full_guth=False, symmetric=True, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Indice de Similitude-Guth (ISG) similarity.

This is an implementation of Bouchard & Pouyez's Indice de Similitude-Guth (ISG) [BP80]. At its heart, ISG is Jaccard similarity, but limits on token matching are added according to part of Guth's matching criteria [Gut76].

[BP80] is limited in its implementation details. Based on the examples given in the paper, it appears that only the first 4 of Guth's rules are considered (a letter in the first string must match a letter in the second string appearing in the same position, an adjacent position, or two positions ahead). It also appears that the distance in the paper is the greater of the distance from string 1 to string 2 and the distance from string 2 to string 1.

These qualities can be specified as parameters. At initialization, specify full_guth=True to apply all of Guth's rules and symmetric=False to calculate only the distance from string 1 to string 2.

New in version 0.4.1.

Initialize ISG instance.

Parameters
  • full_guth (bool) -- Whether to apply all of Guth's matching rules

  • symmetric (bool) -- Whether to calculate the symmetric distance

  • **kwargs -- Arbitrary keyword arguments

New in version 0.4.1.

sim(src, tar)[source]

Return the Indice de Similitude-Guth (ISG) similarity of two words.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The ISG similarity

Return type

float

Examples

>>> cmp = ISG()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.5
>>> cmp.sim('aluminum', 'Catalan')
0.15384615384615385
>>> cmp.sim('ATCG', 'TAGC')
1.0

New in version 0.4.1.

class abydos.distance.Inclusion(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Inclusion distance.

The INC Programme, developed by [BP80] designates two terms as being "included" when:

  • One name is shorter than the other

  • There are at least 3 common characters

  • There is at most one difference, disregarding unmatching prefixes and suffixes

In addition to these rules, this implementation considers two terms as being "included" if they are identical.

The return value, though a float, can only take one of two values: 0.0, indicating inclusion, or 1.0, indication non-inclusion.

New in version 0.4.1.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

dist(src, tar)[source]

Return the INClusion Programme value of two words.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The INC Programme distance

Return type

float

Examples

>>> cmp = Inclusion()
>>> cmp.dist('cat', 'hat')
1.0
>>> cmp.dist('Niall', 'Neil')
1.0
>>> cmp.dist('aluminum', 'Catalan')
1.0
>>> cmp.dist('ATCG', 'TAGC')
1.0

New in version 0.4.1.

class abydos.distance.Guth(tokenizer=None, **kwargs)[source]

Bases: abydos.distance._distance._Distance

Guth matching.

Guth matching [Gut76] uses a simple positional matching rule list to determine whether two names match. Following the original, the sim_score() method returns only 1.0 for matching or 0.0 for non-matching.

The \(.sim\) mathod instead penalizes more distant matches and never outrightly declares two names a non-matching unless no matches can be made in the two strings.

Tokens other than single characters can be matched by specifying a tokenizer during initialization or setting the qval parameter.

New in version 0.4.1.

Initialize Guth instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-gram. Using this parameter and tokenizer=None will cause the instance to use the QGram tokenizer with this q value.

New in version 0.4.1.

sim(src, tar)[source]

Return the relative Guth similarity of two strings.

This deviates from the algorithm described in [Gut76] in that more distant matches are penalized, so that less similar terms score lower that more similar terms.

If no match is found for a particular token in the source string, this does not result in an automatic 0.0 score. Rather, the score is further penalized towards 0.0.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Relative Guth matching score

Return type

float

Examples

>>> cmp = Guth()
>>> cmp.sim('cat', 'hat')
0.8666666666666667
>>> cmp.sim('Niall', 'Neil')
0.8800000000000001
>>> cmp.sim('aluminum', 'Catalan')
0.4
>>> cmp.sim('ATCG', 'TAGC')
0.8

New in version 0.4.1.

sim_score(src, tar)[source]

Return the Guth matching score of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

Guth matching score (1.0 if matching, otherwise 0.0)

Return type

float

Examples

>>> cmp = Guth()
>>> cmp.sim_score('cat', 'hat')
1.0
>>> cmp.sim_score('Niall', 'Neil')
1.0
>>> cmp.sim_score('aluminum', 'Catalan')
0.0
>>> cmp.sim_score('ATCG', 'TAGC')
1.0

New in version 0.4.1.

class abydos.distance.VPS(**kwargs)[source]

Bases: abydos.distance._distance._Distance

Victorian Panel Study (VPS) score.

VPS score is presented in [Schurer07].

New in version 0.4.1.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the Victorian Panel Study score of two words.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The VPS score

Return type

float

Examples

>>> cmp = VPS()
>>> cmp.sim('cat', 'hat')
0.5
>>> cmp.sim('Niall', 'Neil')
0.3
>>> cmp.sim('aluminum', 'Catalan')
0.14285714285714285
>>> cmp.sim('ATCG', 'TAGC')
0.3333333333333333

New in version 0.4.1.

class abydos.distance.LIG3(**kwargs)[source]

Bases: abydos.distance._distance._Distance

LIG3 similarity.

[SD02] proposes three Levenshtein-ISG-Guth hybrid similarity measures: LIG1, LIG2, and LIG3. Of these, LIG1 is identical to ISG and LIG2 is identical to normalized Levenshtein similarity. Only LIG3 is a novel measure, defined as:

\[sim_{LIG3}(X, Y) = \frac{2I}{2I+C}\]

Here, I is the number of exact matches between the two words, truncated to the length of the shorter word, and C is the Levenshtein distance between the two words.

New in version 0.4.1.

Initialize _Distance instance.

Parameters

**kwargs -- Arbitrary keyword arguments

New in version 0.4.0.

sim(src, tar)[source]

Return the LIG3 similarity of two words.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

The LIG3 similarity

Return type

float

Examples

>>> cmp = LIG3()
>>> cmp.sim('cat', 'hat')
0.8
>>> cmp.sim('Niall', 'Neil')
0.5714285714285714
>>> cmp.sim('aluminum', 'Catalan')
0.0
>>> cmp.sim('ATCG', 'TAGC')
0.0

New in version 0.4.1.

class abydos.distance.SSK(tokenizer=None, ssk_lambda=0.9, **kwargs)[source]

Bases: abydos.distance._token_distance._TokenDistance

String subsequence kernel (SSK) similarity.

This is based on [LSShaweTaylor+02].

New in version 0.4.1.

Initialize SSK instance.

Parameters
  • tokenizer (_Tokenizer) -- A tokenizer instance from the abydos.tokenizer package

  • ssk_lambda (float or Iterable) -- A value in the range (0.0, 1.0) used for discouting gaps between characters according to the method described in [LSShaweTaylor+02]. To supply multiple values of lambda, provide an Iterable of numeric values, such as (0.5, 0.05) or np.arange(0.05, 0.5, 0.05)

  • **kwargs -- Arbitrary keyword arguments

Other Parameters

qval (int) -- The length of each q-skipgram. Using this parameter and tokenizer=None will cause the instance to use the QGramskipgrams tokenizer with this q value.

New in version 0.4.1.

sim(src, tar)[source]

Return the normalized SSK similarity of two strings.

Parameters
  • src (str) -- Source string (or QGrams/Counter objects) for comparison

  • tar (str) -- Target string (or QGrams/Counter objects) for comparison

Returns

Normalized string subsequence kernel similarity

Return type

float

Examples

>>> cmp = SSK()
>>> cmp.sim('cat', 'hat')
0.3558718861209964
>>> cmp.sim('Niall', 'Neil')
0.4709007822130597
>>> cmp.sim('aluminum', 'Catalan')
0.13760157193822603
>>> cmp.sim('ATCG', 'TAGC')
0.6140899528060498

New in version 0.4.1.

sim_score(src, tar)[source]

Return the SSK similarity of two strings.

Parameters
  • src (str) -- Source string for comparison

  • tar (str) -- Target string for comparison

Returns

String subsequence kernel similarity

Return type

float

Examples

>>> cmp = SSK()
>>> cmp.dist_abs('cat', 'hat')
0.6441281138790036
>>> cmp.dist_abs('Niall', 'Neil')
0.5290992177869402
>>> cmp.dist_abs('aluminum', 'Catalan')
0.862398428061774
>>> cmp.dist_abs('ATCG', 'TAGC')
0.38591004719395017

New in version 0.4.1.