# 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_ii.
Pearson II similarity
"""
from ._pearson_chi_squared import PearsonChiSquared
__all__ = ['PearsonII']
[docs]class PearsonII(PearsonChiSquared):
r"""Pearson II similarity.
For two sets X and Y and a population N, the Pearson II
similarity :cite:`Pearson:1913`, Pearson's coefficient of mean square
contingency, is
.. math::
corr_{PearsonII} = \sqrt{\frac{\chi^2}{|N|+\chi^2}}
where
.. math::
\chi^2 = sim_{PearsonChiSquared}(X, Y) =
\frac{|N| \cdot (|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|)^2}
{|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
\chi^2 = sim_{PearsonChiSquared} =
\frac{n \cdot (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 PearsonII 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(PearsonII, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def sim_score(self, src, tar):
"""Return the Pearson II similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Pearson II similarity
Examples
--------
>>> cmp = PearsonII()
>>> cmp.sim_score('cat', 'hat')
0.44537605041688455
>>> cmp.sim_score('Niall', 'Neil')
0.3392961347892176
>>> cmp.sim_score('aluminum', 'Catalan')
0.10758552665334761
>>> cmp.sim_score('ATCG', 'TAGC')
0.006418353030552324
.. versionadded:: 0.4.0
"""
if src == tar:
return 2 ** 0.5 / 2
chi2 = super(PearsonII, self).sim_score(src, tar)
return (chi2 / (self._population_unique_card() + chi2)) ** 0.5
[docs] def sim(self, src, tar):
"""Return the normalized Pearson II similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Normalized Pearson II similarity
Examples
--------
>>> cmp = PearsonII()
>>> cmp.sim('cat', 'hat')
0.6298568508557214
>>> cmp.sim('Niall', 'Neil')
0.47983719547968123
>>> cmp.sim('aluminum', 'Catalan')
0.15214891090821628
>>> cmp.sim('ATCG', 'TAGC')
0.009076921903905551
.. versionadded:: 0.4.0
"""
return self.sim_score(src, tar) * 2 / 2 ** 0.5
if __name__ == '__main__':
import doctest
doctest.testmod()