# Copyright 2014-2020 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._tversky.
Tversky index
"""
from typing import Any, Optional, cast
from ._token_distance import _TokenDistance
from ..tokenizer import _Tokenizer
__all__ = ['Tversky']
[docs]
class Tversky(_TokenDistance):
r"""Tversky index.
The Tversky index :cite:`Tversky:1977` is defined as:
For two sets X and Y:
.. math::
sim_{Tversky}(X, Y) = \frac{|X \cap Y|}
{|X \cap Y| + \alpha|X - Y| + \beta|Y - X|}
:math:`\alpha = \beta = 1` is equivalent to the Jaccard & Tanimoto
similarity coefficients.
:math:`\alpha = \beta = 0.5` is equivalent to the Sørensen-Dice
similarity coefficient :cite:`Dice:1945,Sorensen:1948`.
Unequal α and β will tend to emphasize one or the other set's
contributions:
- :math:`\alpha > \beta` emphasizes the contributions of X over Y
- :math:`\alpha < \beta` emphasizes the contributions of Y over X)
Parameter values' relation to 1 emphasizes different types of
contributions:
- :math:`\alpha` and :math:`\beta > 1` emphsize unique contributions
over the intersection
- :math:`\alpha` and :math:`\beta < 1` emphsize the intersection over
unique contributions
The symmetric variant is defined in :cite:`Jiminez:2013`. This is activated
by specifying a bias parameter.
.. versionadded:: 0.3.6
"""
def __init__(
self,
alpha: float = 1.0,
beta: float = 1.0,
bias: Optional[float] = None,
tokenizer: Optional[_Tokenizer] = None,
intersection_type: str = 'crisp',
**kwargs: Any
) -> None:
"""Initialize Tversky instance.
Parameters
----------
alpha : float
Tversky index parameter as described above
beta : float
Tversky index parameter as described above
bias : float
The symmetric Tversky index bias parameter
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(Tversky, self).__init__(
tokenizer=tokenizer, intersection_type=intersection_type, **kwargs
)
self.set_params(alpha=alpha, beta=beta, bias=bias)
[docs]
def sim(self, src: str, tar: str) -> float:
"""Return the Tversky index 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
Tversky similarity
Raises
------
ValueError
Unsupported weight assignment; alpha and beta must be greater than
or equal to 0.
Examples
--------
>>> cmp = Tversky()
>>> cmp.sim('cat', 'hat')
0.3333333333333333
>>> cmp.sim('Niall', 'Neil')
0.2222222222222222
>>> cmp.sim('aluminum', 'Catalan')
0.0625
>>> cmp.sim('ATCG', 'TAGC')
0.0
.. versionadded:: 0.1.0
.. versionchanged:: 0.3.6
Encapsulated in class
"""
if self.params['alpha'] < 0 or self.params['beta'] < 0:
raise ValueError(
'Unsupported weight assignment; alpha and beta '
+ 'must be greater than or equal to 0.'
)
if src == tar:
return 1.0
elif not src or not tar:
return 0.0
self._tokenize(src, tar)
q_src_mag = self._src_only_card()
q_tar_mag = self._tar_only_card()
q_intersection_mag = self._intersection_card()
if not self._src_tokens or not self._tar_tokens:
return 0.0
if self.params['bias'] is None:
return cast(
float,
q_intersection_mag
/ (
q_intersection_mag
+ self.params['alpha'] * q_src_mag
+ self.params['beta'] * q_tar_mag
),
)
a_val, b_val = sorted((q_src_mag, q_tar_mag))
c_val = q_intersection_mag + self.params['bias']
return cast(
float,
c_val
/ (
self.params['beta']
* (
self.params['alpha'] * a_val
+ (1 - self.params['alpha']) * b_val
)
+ c_val
),
)
if __name__ == '__main__':
import doctest
doctest.testmod()