# 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._jensen_shannon.
Jensen-Shannon divergence
"""
from math import log
from ._token_distance import _TokenDistance
__all__ = ['JensenShannon']
[docs]class JensenShannon(_TokenDistance):
r"""Jensen-Shannon divergence.
Jensen-Shannon divergence :cite:`Dagan:1999` of two multi-sets X and Y is
.. math::
\begin{array}{rl}
dist_{JS}(X, Y) &= log 2 + \frac{1}{2} \sum_{i \in X \cap Y}
h(p(X_i) + p(Y_i)) - h(p(X_i)) - h(p(Y_i))
h(x) &= -x log x
p(X_i \in X) &= \frac{|X_i|}{|X|}
\end{array}
.. versionadded:: 0.4.0
"""
def __init__(self, tokenizer=None, intersection_type='crisp', **kwargs):
"""Initialize JensenShannon 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
.. versionadded:: 0.4.0
"""
super(JensenShannon, self).__init__(
tokenizer=tokenizer, intersection_type=intersection_type, **kwargs
)
[docs] def dist_abs(self, src, tar):
"""Return the Jensen-Shannon divergence of two strings.
Parameters
----------
src : str
Source string for comparison
tar : str
Target string for comparison
Returns
-------
float
Jensen-Shannon divergence
Examples
--------
>>> cmp = JensenShannon()
>>> cmp.dist_abs('cat', 'hat')
0.3465735902799726
>>> cmp.dist_abs('Niall', 'Neil')
0.44051045978517045
>>> cmp.dist_abs('aluminum', 'Catalan')
0.6115216713968132
>>> cmp.dist_abs('ATCG', 'TAGC')
0.6931471805599453
.. versionadded:: 0.4.0
"""
if src == tar:
return 0.0
self._tokenize(src, tar)
def entropy(prob):
"""Return the entropy of prob."""
if not prob:
return 0.0
return -(prob * log(prob))
src_total = sum(self._src_tokens.values())
tar_total = sum(self._tar_tokens.values())
diverg = log(2)
for key in self._intersection().keys():
p_src = self._src_tokens[key] / src_total
p_tar = self._tar_tokens[key] / tar_total
diverg += (
entropy(p_src + p_tar) - entropy(p_src) - entropy(p_tar)
) / 2
return diverg
[docs] def dist(self, src, tar):
"""Return the normalized Jensen-Shannon distance of two strings.
Parameters
----------
src : str
Source string for comparison
tar : str
Target string for comparison
Returns
-------
float
Normalized Jensen-Shannon distance
Examples
--------
>>> cmp = JensenShannon()
>>> cmp.dist('cat', 'hat')
0.49999999999999994
>>> cmp.dist('Niall', 'Neil')
0.6355222557917826
>>> cmp.dist('aluminum', 'Catalan')
0.8822392827203127
>>> cmp.dist('ATCG', 'TAGC')
1.0
.. versionadded:: 0.4.0
"""
return self.dist_abs(src, tar) / log(2)
if __name__ == '__main__':
import doctest
doctest.testmod()