selector.measures.similarity

Similarity Module.

selector.measures.similarity.modified_tanimoto(a: array, b: array) → float

Compute the modified tanimoto coefficient from bitstring vectors of data points A and B.

Adjusts calculation of the Tanimoto coefficient to counter its natural bias towards shorter vectors using a Bernoulli probability model.

\[{mt} = \frac{2-p}{3} T_1 + \frac{1+p}{3} T_0\]

where \(p\) is success probability of independent trials, \(T_1\) is the number of common ‘1’ bits between data points (\(T_1 = | A \cap B |\)), and \(T_0\) is the number of common ‘0’ bits between data points (\(T_0 = |(1-A) \cap (1-B)|\)).

Parameters

andarray of shape (n_features,)

The 1D bitstring feature array of sample \(A\) in an n_features dimensional space.

bndarray of shape (n_features,)

The 1D bitstring feature array of sample \(B\) in an n_features dimensional space.

Returns

mtfloat

Modified tanimoto coefficient between bitstring feature arrays \(A\) and \(B\).

Notes

The equation above has been derived from

\[{mt}_{\alpha} = {\alpha}T_1 + (1-\alpha)T_0\]

where \(\alpha = \frac{2-p}{3}\). This is done so that the expected value of the modified tanimoto, \(E(mt)\), remains constant even as the number of trials \(p\) grows larger.

Fligner, M. A., Verducci, J. S., and Blower, P. E.. (2002) A Modification of the Jaccard-Tanimoto Similarity Index for Diverse Selection of Chemical Compounds Using Binary Strings. Technometrics 44, 110-119.

selector.measures.similarity.pairwise_similarity_bit(X: array, metric: str) → ndarray

Compute pairwise similarity coefficient matrix.

Parameters

Xndarray of shape (n_samples, n_features)

Feature matrix of n_samples samples in n_features dimensional space.

metricstr

The metric used when calculating similarity coefficients between samples in a feature array. Method for calculating similarity coefficient. Options: “tanimoto”, “modified_tanimoto”.

Returns

sndarray of shape (n_samples, n_samples)

A symmetric similarity matrix between each pair of samples in the feature matrix. The diagonal elements are directly computed instead of assuming that they are 1.

selector.measures.similarity.scaled_similarity_matrix(X: array) → ndarray

Compute the scaled similarity matrix.

\[X(i,j) = \frac{X(i,j)}{\sqrt{X(i,i)X(j,j)}}\]

Parameters

Xndarray of shape (n_samples, n_samples)

Similarity matrix of n_samples.

Returns

sndarray of shape (n_samples, n_samples)

A scaled symmetric similarity matrix.

selector.measures.similarity.tanimoto(a: array, b: array) → float

Compute Tanimoto coefficient or index (a.k.a. Jaccard similarity coefficient).

For two binary or non-binary arrays \(A\) and \(B\), Tanimoto coefficient is defined as the size of their intersection divided by the size of their union:

\[T(A, B) = \frac{| A \cap B|}{| A \cup B |} = \frac{| A \cap B|}{|A| + |B| - | A \cap B|} = \frac{A \cdot B}{\|A\|^2 + \|B\|^2 - A \cdot B}\]

where \(A \cdot B = \sum_i{A_i B_i}\) and \(\|A\|^2 = \sum_i{A_i^2}\).

Parameters

andarray of shape (n_features,)

The 1D feature array of sample \(A\) in an n_features dimensional space.

bndarray of shape (n_features,)

The 1D feature array of sample \(B\) in an n_features dimensional space.

Returns

coefffloat

Tanimoto coefficient between feature arrays \(A\) and \(B\).

Bajusz, D., Rácz, A., and Héberger, K.. (2015) Why is Tanimoto index an appropriate choice for fingerprint-based similarity calculations?. Journal of Cheminformatics 7.