# 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._hurlbert.
Hurlbert correlation
"""
from math import ceil, copysign, floor
from ._token_distance import _TokenDistance
__all__ = ['Hurlbert']
[docs]class Hurlbert(_TokenDistance):
r"""Hurlbert correlation.
In :ref:`2x2 confusion table terms <confusion_table>`, where a+b+c+d=n,
Hurlbert's coefficient of interspecific association :cite:`Hurlbert:1969`
is
.. math::
corr_{Hurlbert} =
\frac{ad-bc}{|ad-bc|} \sqrt{\frac{Obs_{\chi^2}-Min_{\chi^2}}
{Max_{\chi^2}-Min_{\chi^2}}}
Where:
.. math::
\begin{array}{lll}
Obs_{\chi^2} &= \frac{(ad-bc)^2n}{(a+b)(a+c)(b+d)(c+d)}
Max_{\chi^2} &= \frac{(a+b)(b+d)n}{(a+c)(c+d)} &\textrm{ when }
ad \geq bc
Max_{\chi^2} &= \frac{(a+b)(a+c)n}{(b+d)(c+d)} &\textrm{ when }
ad < bc \textrm{ and } a \leq d
Max_{\chi^2} &= \frac{(b+d)(c+d)n}{(a+b)(a+c)} &\textrm{ when }
ad < bc \textrm{ and } a > d
Min_{\chi^2} &= \frac{n^3 (\hat{a} - g(\hat{a}))^2}
{(a+b)(a+c)(c+d)(b+d)}
\textrm{where } \hat{a} &= \frac{(a+b)(a+c)}{n}
\textrm{and } g(\hat{a}) &= \lfloor\hat{a}\rfloor
&\textrm{ when } ad < bc,
\textrm{otherwise } g(\hat{a}) &= \lceil\hat{a}\rceil
\end{array}
.. versionadded:: 0.4.0
"""
def __init__(
self,
alphabet=None,
tokenizer=None,
intersection_type='crisp',
**kwargs
):
"""Initialize Hurlbert 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(Hurlbert, self).__init__(
alphabet=alphabet,
tokenizer=tokenizer,
intersection_type=intersection_type,
**kwargs
)
[docs] def corr(self, src, tar):
"""Return the Hurlbert 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
Hurlbert correlation
Examples
--------
>>> cmp = Hurlbert()
>>> cmp.corr('cat', 'hat')
0.497416003373807
>>> cmp.corr('Niall', 'Neil')
0.32899851514665707
>>> cmp.corr('aluminum', 'Catalan')
0.10144329225459262
>>> cmp.corr('ATCG', 'TAGC')
-1.0
.. versionadded:: 0.4.0
"""
if src == tar:
return 1.0
if not src or not 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
admbc = a * d - b * c
marginals_product = (
max(1.0, a + b)
* max(1.0, a + c)
* max(1.0, b + d)
* max(1.0, c + d)
)
obs_chisq = admbc * admbc * n / marginals_product
if a * d >= b * c:
max_chisq = (
(a + b) * (b + d) * n / (max(1.0, a + c) * max(1.0, c + d))
)
elif a <= d:
max_chisq = (
(a + b) * (a + c) * n / (max(1.0, b + d) * max(1.0, c + d))
)
else:
max_chisq = (
(b + d) * (c + d) * n / (max(1.0, a + b) * max(1.0, a + c))
)
a_hat = (a + b) * (a + c) / n
g_a_hat = ceil(a_hat) if a * d < b * c else floor(a_hat)
min_chisq = n ** 3 * (a_hat - g_a_hat) ** 2 / marginals_product
num = obs_chisq - min_chisq
if num:
return copysign(abs(num / (max_chisq - min_chisq)) ** 0.5, admbc)
return 0.0
[docs] def sim(self, src, tar):
"""Return the Hurlbert 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
Hurlbert similarity
Examples
--------
>>> cmp = Hurlbert()
>>> cmp.sim('cat', 'hat')
0.7487080016869034
>>> cmp.sim('Niall', 'Neil')
0.6644992575733285
>>> cmp.sim('aluminum', 'Catalan')
0.5507216461272963
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.4.0
"""
return (1.0 + self.corr(src, tar)) / 2.0
if __name__ == '__main__':
import doctest
doctest.testmod()