# 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._shape_difference.
Penrose's shape difference
"""
from ._token_distance import _TokenDistance
__all__ = ['Shape']
[docs]class Shape(_TokenDistance):
r"""Penrose's shape difference.
For two sets X and Y and a population N, the Penrose's shape difference
:cite:`Penrose:1952` is
.. math::
dist_{Shape}(X, Y) =
\frac{1}{|N|}\cdot\Big(\sum_{x \in (X \triangle Y)} x^2\Big) -
\Big(\frac{|X \triangle Y|}{|N|}\Big)^2
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
sim_{Shape} =
\frac{1}{n}\Big(\sum_{x \in b} x^2 + \sum_{x \in c} x^2\Big) -
\Big(\frac{b+c}{n}\Big)^2
In :cite:`IBM:2017`, the formula is instead
:math:`\frac{n(b+c)-(b-c)^2}{n^2}`, but it is clear from
:cite:`Penrose:1952` that this should not be an assymmetric value with
respect to the ordering of the two sets, among other errors in this
formula. Meanwhile, :cite:`Deza:2016` gives the formula
:math:`\sqrt{\sum((x_i-\bar{x})-(y_i-\bar{y}))^2}`.
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize Shape 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(Shape, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def dist(self, src, tar):
"""Return the Penrose's shape difference 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
Shape ifference
Examples
--------
>>> cmp = Shape()
>>> cmp.sim('cat', 'hat')
0.994923990004165
>>> cmp.sim('Niall', 'Neil')
0.9911511479591837
>>> cmp.sim('aluminum', 'Catalan')
0.9787090754188811
>>> cmp.sim('ATCG', 'TAGC')
0.9874075905872554
.. versionadded:: 0.4.0
"""
if src == tar:
return 0.0
self._tokenize(src, tar)
symdiff = self._symmetric_difference().values()
dist = sum(symdiff)
dist_sq = sum(_ ** 2 for _ in symdiff)
n = self._population_unique_card()
return dist_sq / n - (dist / n) ** 2
if __name__ == '__main__':
import doctest
doctest.testmod()