rand_binary_similarity#

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

Rand similarity for vectors of binary values.

Computes the Rand similarity [1] [2] (known as All-Bit [3] or Sokal-Michener) for binary data between two input arrays or sparse matrices, using the formula:

\[sim(a, b) = \frac{|a+d|}{n}\]

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

  • \(d\) - both are 0 (\(~|x \cap y|\), common “off” bits)

  • \(n\) - length of passed vectors

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 – Rand similarity between vec_a and vec_b.

Return type:

float

References

Examples

>>> from skfp.distances import rand_binary_similarity
>>> import numpy as np
>>> vec_a = np.array([1, 0, 1])
>>> vec_b = np.array([1, 0, 0])
>>> sim = rand_binary_similarity(vec_a, vec_b)
>>> sim
0.6666666666666666

>>> from scipy.sparse import csr_array
>>> vec_a = csr_array([[1, 0, 1]])
>>> vec_b = csr_array([[1, 0, 0]])
>>> sim = rand_binary_similarity(vec_a, vec_b)
>>> sim
0.6666666666666666