# 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()