Source code for abydos.distance._pearson_ii

# Copyright 2018-2020 by Christopher C. Little.
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"""abydos.distance._pearson_ii.

Pearson II similarity
"""

from ._pearson_chi_squared import PearsonChiSquared

__all__ = ['PearsonII']


[docs]class PearsonII(PearsonChiSquared): r"""Pearson II similarity. For two sets X and Y and a population N, the Pearson II similarity :cite:`Pearson:1913`, Pearson's coefficient of mean square contingency, is .. math:: corr_{PearsonII} = \sqrt{\frac{\chi^2}{|N|+\chi^2}} where .. math:: \chi^2 = sim_{PearsonChiSquared}(X, Y) = \frac{|N| \cdot (|X \cap Y| \cdot |(N \setminus X) \setminus Y| - |X \setminus Y| \cdot |Y \setminus X|)^2} {|X| \cdot |Y| \cdot |N \setminus X| \cdot |N \setminus Y|} In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n, this is .. math:: \chi^2 = sim_{PearsonChiSquared} = \frac{n \cdot (ad-bc)^2}{(a+b)(a+c)(b+d)(c+d)} .. versionadded:: 0.4.0 """ def __init__( self, alphabet=None, tokenizer=None, intersection_type='crisp', **kwargs ): """Initialize PearsonII 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(PearsonII, self).__init__( alphabet=alphabet, tokenizer=tokenizer, intersection_type=intersection_type, **kwargs )
[docs] def sim_score(self, src, tar): """Return the Pearson II 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 Pearson II similarity Examples -------- >>> cmp = PearsonII() >>> cmp.sim_score('cat', 'hat') 0.44537605041688455 >>> cmp.sim_score('Niall', 'Neil') 0.3392961347892176 >>> cmp.sim_score('aluminum', 'Catalan') 0.10758552665334761 >>> cmp.sim_score('ATCG', 'TAGC') 0.006418353030552324 .. versionadded:: 0.4.0 """ if src == tar: return 2 ** 0.5 / 2 chi2 = super(PearsonII, self).sim_score(src, tar) return (chi2 / (self._population_unique_card() + chi2)) ** 0.5
[docs] def sim(self, src, tar): """Return the normalized Pearson II 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 Pearson II similarity Examples -------- >>> cmp = PearsonII() >>> cmp.sim('cat', 'hat') 0.6298568508557214 >>> cmp.sim('Niall', 'Neil') 0.47983719547968123 >>> cmp.sim('aluminum', 'Catalan') 0.15214891090821628 >>> cmp.sim('ATCG', 'TAGC') 0.009076921903905551 .. versionadded:: 0.4.0 """ return self.sim_score(src, tar) * 2 / 2 ** 0.5
if __name__ == '__main__': import doctest doctest.testmod()