ct4_binary_similarity

skfp.distances.ct4_binary_similarity(vec_a: ndarray | csr_array, vec_b: ndarray | csr_array) → float

Consonni–Todeschini 4 similarity for vectors of binary values.

Computes the Consonni–Todeschini 4 similarity [1] [2] [3] for binary data between two input arrays or sparse matrices, using the formula:

\[sim(a, b) = \frac{\log (1 + |a \cap b|)}{\log (1 + |a \cup b|)} = \frac{\log (1 + |a \cap b|)}{\log (1 + |a| + |b| - |a \cap b|)}\]

The calculated similarity falls within the range \([0, 1]\). Passing all-zero vectors to this function results in similarity of 1.

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 – CT4 similarity between vec_a and vec_b.

Return type:

float

References

[1]

V. Consonni, R. Todeschini “New similarity coefficients for binary data” MATCH Commun.Math.Comput.Chem.. 68. 581-592.

[2]

Todeschini, Roberto, Davide Ballabio, and Viviana Consonni “Distances and similarity measures in chemometrics and chemoinformatics.” Encyclopedia of Analytical Chemistry: Applications, Theory and Instrumentation (2006): 1-40.

[3]

Todeschini, Roberto, et al. “Similarity coefficients for binary chemoinformatics data: overview and extended comparison using simulated and real data sets.” J. Chem. Inf. Model. 2012, 52, 11, 2884–2901

Examples

>>> from skfp.distances import ct4_binary_similarity
>>> import numpy as np
>>> vec_a = np.array([1, 0, 1])
>>> vec_b = np.array([1, 0, 1])
>>> sim = ct4_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 = ct4_binary_similarity(vec_a, vec_b)
>>> sim
1.0