iSIM-sigma: efficient standard deviation calculation for molecular similarity.

The average and variance of the molecular similarities in a set is high-value and useful information for cheminformatics tasks like chemical space exploration and subset selection. However, the calculation of the variance of the complete similarity matrix has a quadratic complexity, ( ). As the sizes of molecular libraries constantly increase, this pairwise approach is unfeasible. In this work, we present an alternative to obtaining the exact standard deviation of the molecular similarities in a set (with molecules and features) for the Russell-Rao (RR) and Sokal-Michener (SM) similarity indexes in ( ) complexity. Additionally, we present a highly accurate approximation with linear complexity, ( ), based on the sampling of representative molecules from the set. The proposed approximation can be extended to other similarity indexes, including the popular Jaccard-Tanimoto (JT). With only the sampling of 50 molecules, the proposed method can estimate the standard deviation of the similarities in a set with RMSE lower than 0.01 for sets of up to 50,000 molecules. In comparison, random sampling does not warrant a good approximation as shown in our results.