# Copyright 2014-2020 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._jaccard.
Jaccard similarity coefficient, distance, & Tanimoto coefficient
"""
from math import log2
from typing import Any, Optional
from ._tversky import Tversky
from ..tokenizer import _Tokenizer
__all__ = ['Jaccard']
[docs]class Jaccard(Tversky):
r"""Jaccard similarity.
For two sets X and Y, the Jaccard similarity coefficient
:cite:`Jaccard:1901,Ruzicka:1958` is
.. math::
sim_{Jaccard}(X, Y) =
\frac{|X \cap Y|}{|X \cup Y|}`.
This is identical to the Tanimoto similarity coefficient
:cite:`Tanimoto:1958`
and the Tversky index :cite:`Tversky:1977` for
:math:`\alpha = \beta = 1`.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{Jaccard} =
\frac{a}{a+b+c}
Notes
-----
The multiset variant is termed Ellenberg similarity :cite:`Ellenberg:1956`.
.. versionadded:: 0.3.6
"""
def __init__(
self,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
**kwargs: Any
) -> None:
"""Initialize Jaccard instance.
Parameters
----------
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(Jaccard, self).__init__(
alpha=1,
beta=1,
bias=None,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def sim(self, src: str, tar: str) -> float:
r"""Return the Jaccard 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
Jaccard similarity
Examples
--------
>>> cmp = Jaccard()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.2222222222222222
>>> cmp.sim('aluminum', 'Catalan')
0.0625
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.1.0
.. versionchanged:: 0.3.6
Encapsulated in class
"""
return super(Jaccard, self).sim(src, tar)
[docs] def tanimoto_coeff(self, src: str, tar: str) -> float:
"""Return the Tanimoto distance between two strings.
Tanimoto distance :cite:`Tanimoto:1958` is
:math:`-log_{2} sim_{Tanimoto}(X, Y)`.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for comparison
tar : str
Target string (or QGrams/Counter objects) for comparison
Returns
-------
float
Tanimoto distance
Examples
--------
>>> cmp = Jaccard()
>>> cmp.tanimoto_coeff('cat', 'hat')
-1.5849625007211563
>>> cmp.tanimoto_coeff('Niall', 'Neil')
-2.1699250014423126
>>> cmp.tanimoto_coeff('aluminum', 'Catalan')
-4.0
>>> cmp.tanimoto_coeff('ATCG', 'TAGC')
-inf
.. versionadded:: 0.1.0
.. versionchanged:: 0.3.6
Encapsulated in class
"""
coeff = self.sim(src, tar)
if coeff != 0:
return log2(coeff)
return float('-inf')
if __name__ == '__main__':
import doctest
doctest.testmod()