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# Copyright 2019-2020 by Christopher C. Little. |
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# This file is part of Abydos. |
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# |
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# Abydos is free software: you can redistribute it and/or modify |
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# it under the terms of the GNU General Public License as published by |
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# the Free Software Foundation, either version 3 of the License, or |
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# (at your option) any later version. |
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# |
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# Abydos is distributed in the hope that it will be useful, |
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# but WITHOUT ANY WARRANTY; without even the implied warranty of |
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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# GNU General Public License for more details. |
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# |
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# You should have received a copy of the GNU General Public License |
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# along with Abydos. If not, see <http://www.gnu.org/licenses/>. |
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"""abydos.distance._scott_pi. |
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Scott's Pi correlation |
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""" |
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from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union |
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from ._token_distance import _TokenDistance |
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from ..tokenizer import _Tokenizer |
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__all__ = ['ScottPi'] |
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class ScottPi(_TokenDistance): |
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r"""Scott's Pi correlation. |
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For two sets X and Y and a population N, Scott's :math:`\pi` correlation |
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:cite:`Scott:1955` is |
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.. math:: |
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corr_{Scott_\pi}(X, Y) = \pi = |
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\frac{p_o - p_e^\pi}{1 - p_e^\pi} |
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where |
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.. math:: |
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\begin{array}{ll} |
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p_o &= \frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|} |
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p_e^\pi &= \Big(\frac{|X| + |Y|}{2 \cdot |N|}\Big)^2 + |
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\Big(\frac{|N \setminus X| + |N \setminus Y|}{2 \cdot |N|}\Big)^2 |
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\end{array} |
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In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n, |
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this is |
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.. math:: |
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\begin{array}{ll} |
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p_o &= \frac{a+d}{n} |
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p_e^\pi &= \Big(\frac{2a+b+c}{2n}\Big)^2 + |
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\Big(\frac{2d+b+c}{2n}\Big)^2 |
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\end{array} |
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.. versionadded:: 0.4.0 |
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""" |
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def __init__( |
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self, |
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alphabet: Optional[ |
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Union[TCounter[str], Sequence[str], Set[str], int] |
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] = None, |
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tokenizer: Optional[_Tokenizer] = None, |
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intersection_type: str = 'crisp', |
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**kwargs: Any |
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) -> None: |
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"""Initialize ScottPi instance. |
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Parameters |
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---------- |
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alphabet : Counter, collection, int, or None |
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This represents the alphabet of possible tokens. |
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See :ref:`alphabet <alphabet>` description in |
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:py:class:`_TokenDistance` for details. |
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tokenizer : _Tokenizer |
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A tokenizer instance from the :py:mod:`abydos.tokenizer` package |
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intersection_type : str |
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Specifies the intersection type, and set type as a result: |
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See :ref:`intersection_type <intersection_type>` description in |
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:py:class:`_TokenDistance` for details. |
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**kwargs |
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Arbitrary keyword arguments |
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Other Parameters |
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---------------- |
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qval : int |
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The length of each q-gram. Using this parameter and tokenizer=None |
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will cause the instance to use the QGram tokenizer with this |
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q value. |
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metric : _Distance |
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A string distance measure class for use in the ``soft`` and |
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``fuzzy`` variants. |
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threshold : float |
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A threshold value, similarities above which are counted as |
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members of the intersection for the ``fuzzy`` variant. |
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.. versionadded:: 0.4.0 |
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""" |
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super(ScottPi, self).__init__( |
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alphabet=alphabet, |
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tokenizer=tokenizer, |
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intersection_type=intersection_type, |
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**kwargs |
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) |
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def corr(self, src: str, tar: str) -> float: |
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"""Return the Scott's Pi correlation of two strings. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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Returns |
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------- |
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float |
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Scott's Pi correlation |
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Examples |
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-------- |
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>>> cmp = ScottPi() |
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>>> cmp.corr('cat', 'hat') |
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0.49743589743589733 |
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>>> cmp.corr('Niall', 'Neil') |
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0.35914053833129245 |
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>>> cmp.corr('aluminum', 'Catalan') |
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0.10798833377524023 |
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>>> cmp.corr('ATCG', 'TAGC') |
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-0.006418485237489689 |
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.. versionadded:: 0.4.0 |
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""" |
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if src == tar: |
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return 1.0 |
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self._tokenize(src, tar) |
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a = self._intersection_card() |
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b = self._src_only_card() |
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c = self._tar_only_card() |
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d = self._total_complement_card() |
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n = a + b + c + d |
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po = (a + d) / n |
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pe = ((2 * a + b + c) / (2 * n)) ** 2 + ( |
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(2 * d + b + c) / (2 * n) |
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) ** 2 |
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if po != pe: |
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return (po - pe) / (1 - pe) |
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return 0.0 |
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def sim(self, src: str, tar: str) -> float: |
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"""Return the Scott's Pi similarity of two strings. |
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Parameters |
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---------- |
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src : str |
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Source string (or QGrams/Counter objects) for comparison |
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tar : str |
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Target string (or QGrams/Counter objects) for comparison |
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Returns |
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------- |
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float |
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Scott's Pi similarity |
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Examples |
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-------- |
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>>> cmp = ScottPi() |
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>>> cmp.sim('cat', 'hat') |
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0.7487179487179487 |
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>>> cmp.sim('Niall', 'Neil') |
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0.6795702691656462 |
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>>> cmp.sim('aluminum', 'Catalan') |
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0.5539941668876202 |
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>>> cmp.sim('ATCG', 'TAGC') |
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0.49679075738125517 |
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.. versionadded:: 0.4.0 |
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""" |
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return (1.0 + self.corr(src, tar)) / 2.0 |
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if __name__ == '__main__': |
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import doctest |
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doctest.testmod() |
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chrislit /
abydos
