Source code for abydos.distance._steffensen

# Copyright 2019-2020 by Christopher C. Little.
# This file is part of Abydos.
#
# Abydos is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Abydos is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Abydos. If not, see <http://www.gnu.org/licenses/>.

"""abydos.distance._steffensen.

Steffensen similarity
"""

from numpy import array as np_array

from ._token_distance import _TokenDistance

__all__ = ['Steffensen']


[docs]class Steffensen(_TokenDistance): r"""Steffensen similarity. For two sets X and Y and a population N, Steffensen similarity :math:`\psi^2` :cite:`Steffensen:1934` is .. math:: \begin{array}{ll} sim_{Steffensen_{\psi}}(X, Y) = \psi^2 &= \sum_{i \in X}\sum_{j \in Y} p_{ij} \phi_{ij}^2 \\ \\ \phi_{ij}^2 &= \frac{(p_{ij} - p_{i*}p_{*i})^2} {p_{i*}(1-p_{i*})p_{*j}(1-p_{*j})} \end{array} Where each value :math:`p_{ij}` is drawn from the 2x2 contingency table: +-------------------+------------------+-------------------+---------+ | | |s_in| ``tar`` | |s_notin| ``tar`` | | +-------------------+------------------+-------------------+---------+ | |s_in| ``src`` | |s_a| | |s_b| | |s_a+b| | +-------------------+------------------+-------------------+---------+ | |s_notin| ``src`` | |s_c| | |s_d| | |s_c+d| | +-------------------+------------------+-------------------+---------+ | | |s_a+c| | |s_b+d| | |s_n| | +-------------------+------------------+-------------------+---------+ .. |s_in| replace:: :math:`x \in` .. |s_notin| replace:: :math:`x \notin` .. |s_a| replace:: :math:`p_{11} = a` .. |s_b| replace:: :math:`p_{10} = b` .. |s_c| replace:: :math:`p_{01} = c` .. |s_d| replace:: :math:`p_{00} = d` .. |s_n| replace:: :math:`1` .. |s_a+b| replace:: :math:`p_{1*} = a+b` .. |s_a+c| replace:: :math:`p_{*1} = a+c` .. |s_c+d| replace:: :math:`p_{0*} = c+d` .. |s_b+d| replace:: :math:`p_{*0} = b+d` .. versionadded:: 0.4.0 """ def __init__( self, alphabet=None, tokenizer=None, intersection_type='crisp', normalizer='proportional', **kwargs ): """Initialize Steffensen 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(Steffensen, self).__init__( alphabet=alphabet, tokenizer=tokenizer, intersection_type=intersection_type, normalizer=normalizer, **kwargs )
[docs] def sim(self, src, tar): """Return the Steffensen 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 Steffensen similarity Examples -------- >>> cmp = Steffensen() >>> cmp.sim('cat', 'hat') 0.24744247205786737 >>> cmp.sim('Niall', 'Neil') 0.1300991207720166 >>> cmp.sim('aluminum', 'Catalan') 0.011710186806836031 >>> cmp.sim('ATCG', 'TAGC') 4.1196952743871653e-05 .. versionadded:: 0.4.0 """ if src == tar: return 1.0 if not src or not tar: return 0.0 self._tokenize(src, tar) a = self._intersection_card() b = self._src_only_card() c = self._tar_only_card() d = self._total_complement_card() n = a + b + c + d p = np_array([[a, b], [c, d]]) / n psisq = 0.0 for i in range(len(p)): pi_star = p[i, :].sum() for j in range(len(p[i])): pj_star = p[:, j].sum() num = p[i, j] * (p[i, j] - pi_star * pj_star) ** 2 if num: psisq += num / ( pi_star * (1 - pi_star) * pj_star * (1 - pj_star) ) return psisq
if __name__ == '__main__': import doctest doctest.testmod()