abydos/distance/_kendall_tau.py
# 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._kendall_tau.
Kendall's Tau correlation
"""
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['KendallTau']
class KendallTau(_TokenDistance):
r"""Kendall's Tau correlation.
For two sets X and Y and a population N, Kendall's Tau correlation
:cite:`Kendall:1938` is
.. math::
corr_{KendallTau}(X, Y) =
\frac{2 \cdot (|X \cap Y| + |(N \setminus X) \setminus Y| -
|X \triangle Y|)}{|N| \cdot (|N|-1)}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
corr_{KendallTau} =
\frac{2 \cdot (a+d-b-c)}{n \cdot (n-1)}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet: Optional[
Union[TCounter[str], Sequence[str], Set[str], int]
] = None,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
**kwargs: Any
) -> None:
"""Initialize KendallTau 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(KendallTau, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
def corr(self, src: str, tar: str) -> float:
"""Return the Kendall's Tau 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
Kendall's Tau correlation
Examples
--------
>>> cmp = KendallTau()
>>> cmp.corr('cat', 'hat')
0.0025282143508744493
>>> cmp.corr('Niall', 'Neil')
0.00250866630176975
>>> cmp.corr('aluminum', 'Catalan')
0.0024535291823735866
>>> cmp.corr('ATCG', 'TAGC')
0.0024891182526650506
Notes
-----
This correlation is not necessarily bounded to [-1.0, 1.0], but will
typically be within these bounds for real data.
.. 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 = self._population_unique_card()
num = a + d - b - c
if num:
return 2 * num / (n * max(n - 1, 1))
return 0.0
def sim(self, src: str, tar: str) -> float:
"""Return the Kendall's Tau similarity of two strings.
The Tau correlation is first clamped to the range [-1.0, 1.0] before
being converted to a similarity value to ensure that the similarity
is in the range [0.0, 1.0].
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Kendall's Tau similarity
Examples
--------
>>> cmp = KendallTau()
>>> cmp.sim('cat', 'hat')
0.5012641071754372
>>> cmp.sim('Niall', 'Neil')
0.5012543331508849
>>> cmp.sim('aluminum', 'Catalan')
0.5012267645911868
>>> cmp.sim('ATCG', 'TAGC')
0.5012445591263325
.. versionadded:: 0.4.0
"""
score = max(-1.0, min(1.0, self.corr(src, tar)))
return (1.0 + score) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()