# 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._yates_chi_squared.
Yates's Chi-Squared similarity
"""
from math import copysign
from ._token_distance import _TokenDistance
__all__ = ['YatesChiSquared']
[docs]class YatesChiSquared(_TokenDistance):
r"""Yates's Chi-Squared similarity.
For two sets X and Y and a population N, Yates's :math:`\chi^2` similarity
:cite:`Yates:1934` is
.. math::
sim_{Yates_{\chi^2}}(X, Y) =
\frac{|N| \cdot (||X \cap Y| \cdot
|(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|| -
\frac{|N|}{2})^2}
{|X| \cdot |N \setminus X| \cdot |Y| \cdot
|N \setminus Y|}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{Yates_{\chi^2}} =
\frac{n \cdot (|ad-bc| - \frac{n}{2})^2}{(a+b)(c+d)(a+c)(b+d)}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize YatesChiSquared 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(YatesChiSquared, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def sim_score(self, src, tar, signed=False):
"""Return Yates's Chi-Squared similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
signed : bool
If True, negative correlations will carry a negative sign
Returns
-------
float
Yates's Chi-Squared similarity
Examples
--------
>>> cmp = YatesChiSquared()
>>> cmp.sim_score('cat', 'hat')
108.37343852728468
>>> cmp.sim_score('Niall', 'Neil')
56.630055670871954
>>> cmp.sim_score('aluminum', 'Catalan')
1.8574215841854373
>>> cmp.sim_score('ATCG', 'TAGC')
6.960385076156687
.. versionadded:: 0.4.0
"""
if not src or not tar:
return 0.0
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()
admbc = a * d - b * c
num = n * (abs(admbc) - n / 2) ** 2
denom = (
max(1, (a + b))
* max(1, (c + d))
* max(1, (a + c))
* max(1, (b + d))
)
if num:
score = num / denom
if signed:
score = copysign(score, admbc)
return score
return 0.0
[docs] def sim(self, src, tar):
"""Return Yates's normalized Chi-Squared similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Normalized Yates's Chi-Squared similarity
Examples
--------
>>> cmp = YatesChiSquared()
>>> cmp.sim('cat', 'hat')
0.18081199852082455
>>> cmp.sim('Niall', 'Neil')
0.08608296705052738
>>> cmp.sim('aluminum', 'Catalan')
0.0026563223707532654
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
if not src or not tar:
return 0.0
score = self.sim_score(src, tar, signed=True)
if score < 0:
return 0.0
norm = max(self.sim_score(src, src), self.sim_score(tar, tar))
return score / norm
if __name__ == '__main__':
import doctest
doctest.testmod()