# 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_ix.
Kuhns IX correlation
"""
from ._token_distance import _TokenDistance
__all__ = ['KuhnsIX']
[docs]class KuhnsIX(_TokenDistance):
r"""Kuhns IX correlation.
For two sets X and Y and a population N, Kuhns IX correlation
:cite:`Kuhns:1965`, the excess of coefficient of linear correlation over
its independence value (L), is
.. math::
corr_{KuhnsIX}(X, Y) =
\frac{\delta(X, Y)}{\sqrt{|X|\cdot|Y|\cdot(1-\frac{|X|}{|N|})
\cdot(1-\frac{|Y|}{|N|})}}
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::
corr_{KuhnsIX} =
\frac{\delta(a+b, a+c)}{\sqrt{(a+b)(a+c)(1-\frac{a+b}{n})
(1-\frac{a+c}{n})}}
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 KuhnsIX 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(KuhnsIX, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def corr(self, src, tar):
"""Return the Kuhns IX 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
Kuhns IX correlation
Examples
--------
>>> cmp = KuhnsIX()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.36069255713421955
>>> cmp.corr('aluminum', 'Catalan')
0.10821361655002706
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237483954
.. 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()
n = a + b + c + d
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:
marginals_product = (
max(1, a + b) * max(1, a + c) * max(1, b + d) * max(1, c + d)
)
# clamp to [-1.0, 1.0], strictly due to floating point precision
# issues
return max(
-1.0, min(1.0, (delta_ab * n / (marginals_product ** 0.5)))
)
[docs] def sim(self, src, tar):
"""Return the Kuhns IX 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 IX similarity
Examples
--------
>>> cmp = KuhnsIX()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6803462785671097
>>> cmp.sim('aluminum', 'Catalan')
0.5541068082750136
>>> cmp.sim('ATCG', 'TAGC')
0.496790757381258
.. versionadded:: 0.4.0
"""
return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()