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# Copyright 2018-2020 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._digby. |
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Digby 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__ = ['Digby'] |
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class Digby(_TokenDistance): |
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r"""Digby correlation. |
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For two sets X and Y and a population N, Digby's approximation of the |
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tetrachoric correlation coefficient |
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:cite:`Digby:1983` is |
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1 |
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.. math:: |
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corr_{Digby}(X, Y) = |
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\frac{(|X \cap Y| \cdot |(N \setminus X) \setminus Y|)^\frac{3}{4}- |
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(|X \setminus Y| \cdot |Y \setminus X|)^\frac{3}{4}} |
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{(|X \cap Y| \cdot |(N \setminus X) \setminus Y|)^\frac{3}{4} + |
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(|X \setminus Y| \cdot |Y \setminus X|)^\frac{3}{4}} |
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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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corr_{Digby} = |
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\frac{ad^\frac{3}{4}-bc^\frac{3}{4}}{ad^\frac{3}{4}+bc^\frac{3}{4}} |
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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 Digby 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(Digby, 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 Digby 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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Digby correlation |
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Examples |
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-------- |
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>>> cmp = Digby() |
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>>> cmp.corr('cat', 'hat') |
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0.9774244829419212 |
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>>> cmp.corr('Niall', 'Neil') |
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0.9491281473458171 |
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>>> cmp.corr('aluminum', 'Catalan') |
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0.7541039303781305 |
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>>> cmp.corr('ATCG', 'TAGC') |
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-1.0 |
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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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if not src or not 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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num = (a * d) ** 0.75 - (b * c) ** 0.75 |
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if num: |
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return num / ((a * d) ** 0.75 + (b * c) ** 0.75) |
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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 Digby 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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Digby similarity |
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Examples |
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-------- |
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>>> cmp = Digby() |
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>>> cmp.sim('cat', 'hat') |
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0.9887122414709606 |
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>>> cmp.sim('Niall', 'Neil') |
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0.9745640736729085 |
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>>> cmp.sim('aluminum', 'Catalan') |
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0.8770519651890653 |
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>>> cmp.sim('ATCG', 'TAGC') |
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0.0 |
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.. versionadded:: 0.4.0 |
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""" |
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return (1 + self.corr(src, tar)) / 2 |
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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
