# 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._scott_pi.
Scott's Pi correlation
"""
from ._token_distance import _TokenDistance
__all__ = ['ScottPi']
[docs]class ScottPi(_TokenDistance):
r"""Scott's Pi correlation.
For two sets X and Y and a population N, Scott's :math:`\pi` correlation
:cite:`Scott:1955` is
.. math::
corr_{Scott_\pi}(X, Y) = \pi =
\frac{p_o - p_e^\pi}{1 - p_e^\pi}
where
.. math::
\begin{array}{ll}
p_o &= \frac{|X \cap Y| + |(N \setminus X) \setminus Y|}{|N|}
p_e^\pi &= \Big(\frac{|X| + |Y|}{2 \cdot |N|}\Big)^2 +
\Big(\frac{|N \setminus X| + |N \setminus Y|}{2 \cdot |N|}\Big)^2
\end{array}
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
\begin{array}{ll}
p_o &= \frac{a+d}{n}
p_e^\pi &= \Big(\frac{2a+b+c}{2n}\Big)^2 +
\Big(\frac{2d+b+c}{2n}\Big)^2
\end{array}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize ScottPi 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(ScottPi, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def corr(self, src, tar):
"""Return the Scott's Pi correlation 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
Scott's Pi correlation
Examples
--------
>>> cmp = ScottPi()
>>> cmp.corr('cat', 'hat')
0.49743589743589733
>>> cmp.corr('Niall', 'Neil')
0.35914053833129245
>>> cmp.corr('aluminum', 'Catalan')
0.10798833377524023
>>> cmp.corr('ATCG', 'TAGC')
-0.006418485237489689
.. 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()
d = self._total_complement_card()
n = a + b + c + d
po = (a + d) / n
pe = ((2 * a + b + c) / (2 * n)) ** 2 + (
(2 * d + b + c) / (2 * n)
) ** 2
if po != pe:
return (po - pe) / (1 - pe)
return 0.0
[docs] def sim(self, src, tar):
"""Return the Scott's Pi 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
Scott's Pi similarity
Examples
--------
>>> cmp = ScottPi()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6795702691656462
>>> cmp.sim('aluminum', 'Catalan')
0.5539941668876202
>>> cmp.sim('ATCG', 'TAGC')
0.49679075738125517
.. versionadded:: 0.4.0
"""
return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()