# 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._kuhns_xii.
Kuhns XII similarity
"""
from ._token_distance import _TokenDistance
__all__ = ['KuhnsXII']
[docs]class KuhnsXII(_TokenDistance):
r"""Kuhns XII similarity.
For two sets X and Y and a population N, Kuhns XII similarity
:cite:`Kuhns:1965`, the excess of index of independence over its
independence value (I), is
.. math::
sim_{KuhnsXII}(X, Y) =
\frac{|N| \cdot \delta(X, Y)}{|X| \cdot |Y|}
where
.. math::
\delta(X, Y) = |X \cap Y| - \frac{|X| \cdot |Y|}{|N|}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{KuhnsXII} =
\frac{n \cdot \delta(a+b, a+c)}{(a+b)(a+c)}
where
.. math::
\delta(a+b, a+c) = a - \frac{(a+b)(a+c)}{n}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize KuhnsXII 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(KuhnsXII, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def sim_score(self, src, tar):
"""Return the Kuhns XII 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
Kuhns XII similarity
Examples
--------
>>> cmp = KuhnsXII()
>>> cmp.sim_score('cat', 'hat')
97.0
>>> cmp.sim_score('Niall', 'Neil')
51.266666666666666
>>> cmp.sim_score('aluminum', 'Catalan')
9.902777777777779
>>> cmp.sim_score('ATCG', 'TAGC')
-1.0
.. versionadded:: 0.4.0
"""
self._tokenize(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
n = self._population_unique_card()
apbmapc = (a + b) * (a + c)
if not apbmapc:
delta_ab = a
else:
delta_ab = a - apbmapc / n
if not delta_ab:
return 0.0
else:
return max(-1.0, n * delta_ab / ((a + b) * (a + c)))
[docs] def sim(self, src, tar):
"""Return the normalized Kuhns XII 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 Kuhns XII similarity
Examples
--------
>>> cmp = KuhnsXII()
>>> cmp.sim('cat', 'hat')
0.2493573264781491
>>> cmp.sim('Niall', 'Neil')
0.1323010752688172
>>> cmp.sim('aluminum', 'Catalan')
0.012877474353417137
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
score = self.sim_score(src, tar)
minval, maxval = sorted(
[self._intersection_card(), self._total_complement_card()]
)
if score < 0.0:
return min(1.0, (1.0 + score) / 2.0)
norm = 1.0
if minval and maxval:
norm = maxval / minval
return min(1.0, score / norm)
if __name__ == '__main__':
import doctest
doctest.testmod()