# 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._gower_legendre.
Gower & Legendre similarity
"""
from ._token_distance import _TokenDistance
__all__ = ['GowerLegendre']
[docs]class GowerLegendre(_TokenDistance):
r"""Gower & Legendre similarity.
For two sets X and Y and a population N, the Gower & Legendre similarity
:cite:`Gower:1986` is
.. math::
sim_{GowerLegendre}(X, Y) =
\frac{|X \cap Y| + |(N \setminus X) \setminus Y|}
{|X \cap Y| + |(N \setminus X) \setminus Y| +
\theta \cdot |X \triangle Y|}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{GowerLegendre} =
\frac{a+d}{a+\theta(b+c)+d}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
theta=0.5,
**kwargs
):
"""Initialize GowerLegendre 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.
theta : float
The weight to place on the symmetric difference.
**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.theta = theta
super(GowerLegendre, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def sim(self, src, tar):
"""Return the Gower & Legendre 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
Gower & Legendre similarity
Examples
--------
>>> cmp = GowerLegendre()
>>> cmp.sim('cat', 'hat')
0.9974424552429667
>>> cmp.sim('Niall', 'Neil')
0.9955156950672646
>>> cmp.sim('aluminum', 'Catalan')
0.9903536977491961
>>> cmp.sim('ATCG', 'TAGC')
0.993581514762516
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
self._tokenize(src, tar)
apd = self._intersection_card() + self._total_complement_card()
bpc = self._src_only_card() + self._tar_only_card()
return apd / (apd + self.theta * bpc)
if __name__ == '__main__':
import doctest
doctest.testmod()