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# -*- coding: utf-8 -*- |
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# Copyright 2018-2019 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._koppen_i. |
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Köppen I correlation |
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""" |
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from __future__ import ( |
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absolute_import, |
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division, |
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print_function, |
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unicode_literals, |
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) |
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from ._token_distance import _TokenDistance |
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__all__ = ['KoppenI'] |
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class KoppenI(_TokenDistance): |
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r"""Köppen I correlation. |
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For two sets X and Y and an alphabet N, provided that :math:`|X| = |Y|`, |
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Köppen I correlation :cite:`Koppen:1870,Goodman:1959` is |
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.. math:: |
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corr_{KoppenI}(X, Y) = |
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\frac{|X| \cdot |N \setminus X| - |X \setminus Y|} |
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{|X| \cdot |N \setminus X|} |
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To support cases where :math:`|X| \neq |Y|`, this class implements a slight |
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variation, while still providing the expected results when |
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:math:`|X| = |Y|`: |
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.. math:: |
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corr_{KoppenI}(X, Y) = |
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\frac{\frac{|X|+|Y|}{2} \cdot |
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\frac{|N \setminus X|+|N \setminus Y|}{2}- |
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\frac{|X \triangle Y|}{2}} |
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{\frac{|X|+|Y|}{2} \cdot |
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\frac{|N \setminus X|+|N \setminus Y|}{2}} |
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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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sim_{KoppenI} = |
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\frac{\frac{2a+b+c}{2} \cdot \frac{2d+b+c}{2}- |
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\frac{b+c}{2}} |
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{\frac{2a+b+c}{2} \cdot \frac{2d+b+c}{2}} |
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Notes |
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----- |
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In the usual case all of the above values should be proportional to the |
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total number of samples n. I.e., a, b, c, d, & n should all be divided by |
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n prior to calculating the coefficient. This class's default normalizer |
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is, accordingly, 'proportional'. |
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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=None, |
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tokenizer=None, |
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intersection_type='crisp', |
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normalizer='proportional', |
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**kwargs |
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): |
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"""Initialize KoppenI 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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normalizer : str |
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Specifies the normalization type. See :ref:`normalizer <alphabet>` |
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description in :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(KoppenI, 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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normalizer=normalizer, |
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**kwargs |
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) |
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def corr(self, src, tar): |
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"""Return the Köppen I 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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Köppen I correlation |
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Examples |
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-------- |
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>>> cmp = KoppenI() |
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>>> cmp.corr('cat', 'hat') |
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0.49615384615384617 |
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>>> cmp.corr('Niall', 'Neil') |
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0.3575056927658083 |
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>>> cmp.corr('aluminum', 'Catalan') |
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0.1068520131813188 |
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>>> cmp.corr('ATCG', 'TAGC') |
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-0.006418485237483896 |
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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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abac_dbdc_mean_prod = (2 * a + b + c) * (2 * d + b + c) / 4 |
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num = abac_dbdc_mean_prod - (b + c) / 2 |
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if num: |
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return num / abac_dbdc_mean_prod |
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return 0.0 |
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def sim(self, src, tar): |
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"""Return the Köppen I 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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Köppen I similarity |
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Examples |
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-------- |
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>>> cmp = KoppenI() |
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>>> cmp.sim('cat', 'hat') |
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0.7480769230769231 |
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>>> cmp.sim('Niall', 'Neil') |
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0.6787528463829041 |
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>>> cmp.sim('aluminum', 'Catalan') |
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0.5534260065906594 |
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>>> cmp.sim('ATCG', 'TAGC') |
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0.49679075738125805 |
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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
