# Copyright 2019-2020 by Christopher C. Little.
# This file is part of Abydos.
#
# Abydos is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Abydos is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Abydos. If not, see <http://www.gnu.org/licenses/>.
"""abydos.distance._goodman_kruskal_tau_b.
Goodman & Kruskal's Tau B similarity
"""
from ._token_distance import _TokenDistance
__all__ = ['GoodmanKruskalTauB']
[docs]class GoodmanKruskalTauB(_TokenDistance):
r"""Goodman & Kruskal's Tau B similarity.
For two sets X and Y and a population N, Goodman & Kruskal's :math:`\tau_b`
similarity :cite:`Goodman:1954` is
.. math::
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 :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
after each term has been converted to a proportion by dividing by n, this
is
.. math::
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)}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
normalizer='proportional',
**kwargs
):
"""Initialize GoodmanKruskalTauB instance.
Parameters
----------
alphabet : Counter, collection, int, or None
This represents the alphabet of possible tokens.
See :ref:`alphabet <alphabet>` description in
:py:class:`_TokenDistance` for details.
tokenizer : _Tokenizer
A tokenizer instance from the :py:mod:`abydos.tokenizer` package
intersection_type : str
Specifies the intersection type, and set type as a result:
See :ref:`intersection_type <intersection_type>` description in
:py:class:`_TokenDistance` for details.
normalizer : str
Specifies the normalization type. See :ref:`normalizer <alphabet>`
description in :py:class:`_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.
.. versionadded:: 0.4.0
"""
super(GoodmanKruskalTauB, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
normalizer=normalizer,
**kwargs
)
[docs] def sim(self, src, tar):
"""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
-------
float
Goodman & Kruskal's Tau B similarity
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
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
d = self._total_complement_card()
if a + b == 0 or a + c == 0:
return 0.0
fp = (a * a + b * b) / (a + b)
sp = c * c + d * d
if sp:
sp /= c + d
num = fp + sp - (a + c) ** 2 - (b + d) ** 2
if num > 1e-14:
return num / (1 - (a + c) ** 2 - (b + d) ** 2)
return 0.0 # pragma: no cover
if __name__ == '__main__':
import doctest
doctest.testmod()