abydos/distance/_pearson_phi.py
# 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_phi.
Pearson's Phi correlation
"""
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['PearsonPhi']
class PearsonPhi(_TokenDistance):
r"""Pearson's Phi correlation.
For two sets X and Y and a population N, the Pearson's :math:`\phi`
correlation :cite:`Pearson:1900,Pearson:1913,Guilford:1956` is
.. math::
corr_{PearsonPhi}(X, Y) =
\frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|}
{\sqrt{|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|}}
This is also Pearson & Heron I similarity.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
corr_{PearsonPhi} =
\frac{ad-bc}
{\sqrt{(a+b)(a+c)(b+d)(c+d)}}
Notes
-----
In terms of a confusion matrix, this is equivalent to the Matthews
correlation coefficient :py:meth:`ConfusionTable.mcc`.
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet: Optional[
Union[TCounter[str], Sequence[str], Set[str], int]
] = None,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
**kwargs: Any
) -> None:
"""Initialize PearsonPhi 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(PearsonPhi, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
def corr(self, src: str, tar: str) -> float:
"""Return Pearson's Phi 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 Phi correlation
Examples
--------
>>> cmp = PearsonPhi()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.36069255713421955
>>> cmp.corr('aluminum', 'Catalan')
0.10821361655002706
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
if src == tar:
return 1.0
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
d = self._total_complement_card()
ab = self._src_card()
ac = self._tar_card()
num = a * d - b * c
if num:
return num / (ab * ac * (b + d) * (c + d)) ** 0.5
return 0.0
def sim(self, src: str, tar: str) -> float:
"""Return the normalized Pearson's Phi similarity of two strings.
This 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
-------
float
Pearson's Phi similarity
Examples
--------
>>> cmp = PearsonPhi()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6803462785671097
>>> cmp.sim('aluminum', 'Catalan')
0.5541068082750136
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258
.. versionadded:: 0.4.0
"""
return (self.corr(src, tar) + 1.0) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()