# Copyright 2018-2020 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._weighted_jaccard.
Weighted Jaccard similarity
"""
from ._token_distance import _TokenDistance
__all__ = ['WeightedJaccard']
[docs]class WeightedJaccard(_TokenDistance):
r"""Weighted Jaccard similarity.
For two sets X and Y and a weight w, the Weighted Jaccard similarity
:cite:`Legendre:1998` is
.. math::
sim_{Jaccard_w}(X, Y) = \frac{w \cdot |X \cap Y|}
{w \cdot |X \cap Y| + |X \setminus Y| + |Y \setminus X|}
Here, the intersection between the two sets is weighted by w. Compare to
Jaccard similarity (:math:`w = 1`), and to Dice similarity (:math:`w = 2`).
In the default case, the weight of the intersection is 3, following
:cite:`Legendre:1998`.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{Jaccard_w} =
\frac{w\cdot a}{w\cdot a+b+c}
.. versionadded:: 0.4.0
"""
def __init__(
self, tokenizer=None, intersection_type='crisp', weight=3, **kwargs
):
"""Initialize TripleWeightedJaccard 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.
weight : int
The weight to apply to the intersection cardinality. (3, by
default.)
**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
"""
self.weight = weight
super(WeightedJaccard, self).__init__(
tokenizer=tokenizer, intersection_type=intersection_type, **kwargs
)
[docs] def sim(self, src, tar):
"""Return the Triple Weighted 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
Weighted Jaccard similarity
Examples
--------
>>> cmp = WeightedJaccard()
>>> cmp.sim('cat', 'hat')
0.6
>>> cmp.sim('Niall', 'Neil')
0.46153846153846156
>>> cmp.sim('aluminum', 'Catalan')
0.16666666666666666
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
self._tokenize(src, tar)
a = self._intersection_card()
b = self._src_only_card()
c = self._tar_only_card()
return self.weight * a / (self.weight * a + b + c)
if __name__ == '__main__':
import doctest
doctest.testmod()