# Copyright 2018-2020 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._pearson_chi_squared.
Pearson's Chi-Squared similarity
"""
from math import copysign
from ._token_distance import _TokenDistance
__all__ = ['PearsonChiSquared']
[docs]class PearsonChiSquared(_TokenDistance):
r"""Pearson's Chi-Squared similarity.
For two sets X and Y and a population N, the Pearson's :math:`\chi^2`
similarity :cite:`Pearson:1913` is
.. math::
sim_{PearsonChiSquared}(X, Y) =
\frac{|N| \cdot (|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|)^2}
{|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}
This is also Pearson I similarity.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{PearsonChiSquared} =
\frac{n(ad-bc)^2}{(a+b)(a+c)(b+d)(c+d)}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize PearsonChiSquared 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.
**kwargs
Arbitrary keyword arguments
Other Parameters
----------------
qval : int
The 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(PearsonChiSquared, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def sim_score(self, src, tar):
"""Return Pearson's Chi-Squared similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Pearson's Chi-Squared similarity
Examples
--------
>>> cmp = PearsonChiSquared()
>>> cmp.sim_score('cat', 'hat')
193.99489809335964
>>> cmp.sim_score('Niall', 'Neil')
101.99771068526542
>>> cmp.sim_score('aluminum', 'Catalan')
9.19249664336649
>>> cmp.sim_score('ATCG', 'TAGC')
0.032298410951138765
.. 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()
n = self._population_unique_card()
ab = self._src_card()
ac = self._tar_card()
if src == tar:
return float(n)
if not src or not tar:
return 0.0
num = n * (a * d - b * c) ** 2
if num:
return num / (ab * ac * (b + d) * (c + d))
return 0.0
[docs] def corr(self, src, tar):
"""Return Pearson's Chi-Squared correlation of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Pearson's Chi-Squared correlation
Examples
--------
>>> cmp = PearsonChiSquared()
>>> cmp.corr('cat', 'hat')
0.2474424720578567
>>> cmp.corr('Niall', 'Neil')
0.1300991207720222
>>> cmp.corr('aluminum', 'Catalan')
0.011710186806836291
>>> cmp.corr('ATCG', 'TAGC')
-4.1196952743799446e-05
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
score = self.sim_score(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
d = self._total_complement_card()
score /= a + b + c + d
return copysign(score, a * d - b * c)
[docs] def sim(self, src, tar):
"""Return Pearson's normalized Chi-Squared similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Normalized Pearson's Chi-Squared similarity
Examples
--------
>>> cmp = PearsonChiSquared()
>>> cmp.corr('cat', 'hat')
0.2474424720578567
>>> cmp.corr('Niall', 'Neil')
0.1300991207720222
>>> cmp.corr('aluminum', 'Catalan')
0.011710186806836291
>>> cmp.corr('ATCG', 'TAGC')
-4.1196952743799446e-05
.. versionadded:: 0.4.0
"""
return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()