# Source code for abydos.distance._gini_i

# Copyright 2018-2020 by Christopher C. Little.
# This file is part of Abydos.
#
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"""abydos.distance._gini_i.

Gini I correlation
"""

from sys import float_info

from ._token_distance import _TokenDistance

__all__ = ['GiniI']

_epsilon = float_info.epsilon

[docs]class GiniI(_TokenDistance): r"""Gini I correlation. For two sets X and Y and a population N, Gini I correlation :cite:Gini:1912, using the formula from :cite:Goodman:1959, is .. math:: corr_{GiniI}(X, Y) = \frac{\frac{|X \cap Y|+|(N \setminus X) \setminus Y|}{|N|} - \frac{|X| \cdot |Y|}{|N|} + \frac{|N \setminus Y| \cdot |N \setminus X|}{|N|}} {\sqrt{(1-(\frac{|X|}{|N|}^2+\frac{|Y|}{|N|}^2)) \cdot (1-(\frac{|N \setminus Y|}{|N|}^2 + \frac{|N \setminus X|}{|N|}^2))}} In :ref:2x2 confusion table terms <confusion_table>, where a+b+c+d=n, after each term has been converted to a proportion by dividing by n, this is .. math:: corr_{GiniI} = \frac{(a+d)-(a+b)(a+c) + (b+d)(c+d)} {\sqrt{(1-((a+b)^2+(c+d)^2))\cdot(1-((a+c)^2+(b+d)^2))}} .. versionadded:: 0.4.0 """ def __init__( self, alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs ): """Initialize GiniI 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. normalizer : str Specifies the normalization type. See :ref:normalizer <alphabet> 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(GiniI, self).__init__( alphabet=alphabet, tokenizer=tokenizer, intersection_type=intersection_type, normalizer=normalizer, **kwargs )
[docs] def corr(self, src, tar): """Return the Gini I 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 Gini I correlation Examples -------- >>> cmp = GiniI() >>> cmp.corr('cat', 'hat') 0.49722814498933254 >>> cmp.corr('Niall', 'Neil') 0.39649090262533215 >>> cmp.corr('aluminum', 'Catalan') 0.14887105223941113 >>> cmp.corr('ATCG', 'TAGC') -0.006418485237489576 .. versionadded:: 0.4.0 """ self._tokenize(src, tar) a = self._intersection_card() b = self._src_only_card() c = self._tar_only_card() d = self._total_complement_card() return ((a + d) - ((a + b) * (a + c) + (c + d) * (b + d))) / ( (1 + _epsilon - ((a + b) ** 2 + (c + d) ** 2)) * (1 + _epsilon - ((a + c) ** 2 + (b + d) ** 2)) ) ** 0.5
[docs] def sim(self, src, tar): """Return the normalized Gini I 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 Gini I similarity Examples -------- >>> cmp = GiniI() >>> cmp.sim('cat', 'hat') 0.7486140724946663 >>> cmp.sim('Niall', 'Neil') 0.6982454513126661 >>> cmp.sim('aluminum', 'Catalan') 0.5744355261197056 >>> cmp.sim('ATCG', 'TAGC') 0.4967907573812552 .. versionadded:: 0.4.0 """ return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__': import doctest doctest.testmod()