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} {