simpson_binary_similarity

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

Simpson similarity for vectors of binary values.

Computes the Simpson similarity [1] (also known as asymmetric similarity [2] [3] or overlap coefficient [4]) for binary data between two input arrays or sparse matrices using the formula:

\[sim(a, b) = \frac{|a \cap b|}{\min(|a|, |b|)}\]

The calculated similarity falls within the range \([0, 1]\). If any of the vectors is all-zeros, it results in a similarity of 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 – Simpson similarity between vec_a and vec_b.

Return type:

float

References

[1]

Simpson, G.G. “Mammals and the nature of continents.” American Journal of Science, 241: 1-31 (1943).

[2]

Deza M.M., Deza E. “Encyclopedia of Distances.” Springer, Berlin, Heidelberg, 2009.

[3]

RDKit documentation

[4]

Overlap coefficient on Wikipedia

Examples

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