sokal_sneath_2_binary_similarity#

skfp.distances.sokal_sneath_2_binary_similarity(vec_a: ndarray | csr_array, vec_b: ndarray | csr_array) → float#

Sokal-Sneath similarity 2 for vectors of binary values.

Computes the Sokal-Sneath similarity 2 [1] [2] [3] for binary data between two input arrays or sparse matrices, using the formula:

\[sim(a, b) = \frac{|a \cap b|}{|a \cup b| + |a \Delta b} = \frac{|a \cap b|}{2 * |a| + 2 * |b| - 3 * |a \cap b|}\]

where :|a Delta b| is the XOR operation (symmetric difference), i.e. number of bits that are “on” in one vector and “off” in another.

The calculated similarity falls within the range \([0, 1]\). Passing all-zero vectors to this function 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 – Sokal-Sneath similarity 2 between vec_a and vec_b.

Return type:

float

References

Examples

>>> from skfp.distances import sokal_sneath_2_binary_similarity
>>> import numpy as np
>>> vec_a = np.array([1, 1, 1, 1])
>>> vec_b = np.array([1, 1, 0, 0])
>>> sim = sokal_sneath_2_binary_similarity(vec_a, vec_b)
>>> sim
0.3333333333333333

>>> from scipy.sparse import csr_array
>>> vec_a = csr_array([[1, 1, 1, 1]])
>>> vec_b = csr_array([[1, 1, 0, 0]])
>>> sim = sokal_sneath_2_binary_similarity(vec_a, vec_b)
>>> sim
0.3333333333333333