kulczynski_binary_similarity#

skfp.distances.kulczynski_binary_similarity(vec_a: ndarray | csr_array, vec_b: ndarray | csr_array) → float#

Kulczynski similarity for vectors of binary values.

Computes the Kulczynski II similarity [1] [2] [3] for binary data between two input arrays or sparse matrices using the formula:

\[sim(x, y) = \frac{1}{2} \left( \frac{a}{a+b} + \frac{a}{a+c} \right)\]

where \(a\), \(b\) and \(c\) correspond to the number of bit relations between the two vectors:

  • \(a\) - both are 1 (\(|x \cap y|\), common “on” bits)

  • \(b\) - \(x\) is 1, \(y\) is 0

  • \(c\) - \(x\) is 0, \(y\) is 1

Note that this is the second Kulczynski similarity, also used by RDKit. It differs from Kulczynski I similarity from e.g. SciPy.

The calculated similarity falls within the range \([0, 1]\). Passing two all-zero vectors to this function results in a similarity of 1. However, when only one is all-zero (i.e. \(a+b=0\) or \(a+c=0\)), the similarity is 0.

Parameters:

  • vec_a ({ndarray, sparse matrix}) – First binary input array or sparse matrix.

  • vec_b ({ndarray, sparse matrix}) – Second binary input array or sparse matrix.

Returns:

similarity – Kulczynski similarity between vec_a and vec_b.

Return type:

float

References

Examples

>>> from skfp.distances import kulczynski_binary_similarity
>>> import numpy as np
>>> vec_a = np.array([1, 0, 1])
>>> vec_b = np.array([1, 0, 1])
>>> sim = kulczynski_binary_similarity(vec_a, vec_b)
>>> sim
1.0

>>> from scipy.sparse import csr_array
>>> vec_a = csr_array([[1, 0, 1]])
>>> vec_b = csr_array([[1, 0, 1]])
>>> sim = kulczynski_binary_similarity(vec_a, vec_b)
>>> sim
1.0