abydos/distance/_cole.py
# 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._cole.
Cole correlation
"""
from typing import Any, Counter as TCounter, Optional, Sequence, Set, Union
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['Cole']
class Cole(_TokenDistance):
r"""Cole correlation.
For two sets X and Y and a population N, the Cole correlation
:cite:`Cole:1949` has three formulae:
- If :math:`|X \cap Y| \cdot |(N \setminus X) \setminus Y| \geq
|X \setminus Y| \cdot |Y \setminus Y|` then
.. math::
corr_{Cole}(X, Y) =
\frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|}
{(|X \cap Y| + |X \setminus Y|) \cdot
(|X \setminus Y| + |(N \setminus X) \setminus Y|)}
- If :math:`|(N \setminus X) \setminus Y| \geq |X \cap Y|` then
.. math::
corr_{Cole}(X, Y) =
\frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|}
{(|X \cap Y| + |X \setminus Y|) \cdot
(|X \cap Y| + |Y \setminus X|)}
- Otherwise
.. math::
corr_{Cole}(X, Y) =
\frac{|X \cap Y| \cdot |(N \setminus X) \setminus Y| -
|X \setminus Y| \cdot |Y \setminus X|}
{(|X \setminus Y| + |(N \setminus X) \setminus Y|) \cdot
(|Y \setminus X| + |(N \setminus X) \setminus Y|)}
Cole terms this measurement the Coefficient of Interspecific Association.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
this is
.. math::
corr_{Cole} =
\left\{
\begin{array}{ll}
\frac{ad-bc}{(a+b)(b+d)} & \textup{if} ~ad \geq bc \\
\\
\frac{ad-bc}{(a+b)(a+c)} & \textup{if} ~d \geq a \\
\\
\frac{ad-bc}{(b+d)(c+d)} & \textup{otherwise}
\end{array}
\right.
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet: Optional[
Union[TCounter[str], Sequence[str], Set[str], int]
] = None,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
**kwargs: Any
) -> None:
"""Initialize Cole 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(Cole, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
def corr(self, src: str, tar: str) -> float:
"""Return the Cole 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
Cole correlation
Examples
--------
>>> cmp = Cole()
>>> cmp.corr('cat', 'hat')
0.49743589743589745
>>> cmp.corr('Niall', 'Neil')
0.3290543431750107
>>> cmp.corr('aluminum', 'Catalan')
0.10195910195910196
>>> cmp.corr('ATCG', 'TAGC')
-1.0
.. 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()
d = self._total_complement_card()
admbc = a * d - b * c
if admbc == 0.0:
return 0.0
if a * d >= b * c:
return admbc / ((a + b) * (b + d))
if d >= a:
return admbc / ((a + b) * (a + c))
return admbc / ((b + d) * (c + d))
def sim(self, src: str, tar: str) -> float:
"""Return the Cole similarity of two strings.
Parameters
----------
src : str
Source string (or QGrams/Counter objects) for similarity
tar : str
Target string (or QGrams/Counter objects) for similarity
Returns
-------
float
Cole similarity
Examples
--------
>>> cmp = Cole()
>>> cmp.sim('cat', 'hat')
0.7487179487179487
>>> cmp.sim('Niall', 'Neil')
0.6645271715875054
>>> cmp.sim('aluminum', 'Catalan')
0.550979550979551
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
return (1 + self.corr(src, tar)) / 2
if __name__ == '__main__':
import doctest
doctest.testmod()