Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 2: speed, consistency, diversity selection

Abstract

Despite being a central concept in cheminformatics, molecular similarity has so far been limited to the simultaneous comparison of only two molecules at a time and using one index, generally the Tanimoto coefficent. In a recent contribution we have not only introduced a complete mathematical framework for extended similarity calculations, (i.e. comparisons of more than two molecules at a time) but defined a series of novel idices. Part 1 is a detailed analysis of the effects of various parameters on the similarity values calculated by the extended formulas. Their features were revealed by sum of ranking differences and ANOVA. Here, in addition to characterizing several important aspects of the newly introduced similarity metrics, we will highlight their applicability and utility in real-life scenarios using datasets with popular molecular fingerprints. Remarkably, for large datasets, the use of extended similarity measures provides an unprecedented speed-up over “traditional” pairwise similarity matrix calculations. We also provide illustrative examples of a more direct algorithm based on the extended Tanimoto similarity to select diverse compound sets, resulting in much higher levels of diversity than traditional approaches. We discuss the inner and outer consistency of our indices, which are key in practical applications, showing whether then-ary and binary indices rank the data in the same way. We demonstrate the use of the newn-ary similarity metrics ont-distributed stochastic neighbor embedding (t-SNE) plots of datasets of varying diversity, or corresponding to ligands of different pharmaceutical targets, which show that our indices provide a better measure of set compactness than standard binary measures. We also present a conceptual example of the applicability of our indices in agglomerative hierarchical algorithms. The Python code for calculating the extended similarity metrics is freely available at:https://github.com/ramirandaq/MultipleComparisons

Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 1: Theory and characteristics†

“…The framework that we introduced here provides a new alternative, which allows to simultaneously compare more than two dichotomous vectors. This scales in order O(N), presenting a tremendous speed gain: this is further discussed in the accompanying paper [22]. Applications include subset selection, clustering, diversity picking or we can even apply this methodology to estimate the diversities of entire compound libraries.…”

“…The theoretical SRD distributions were defined for different sample sizes up to 13. The theoretical SRD can be well approximated with a Gaussian distribution, if the (22)…”

Molecular Dynamics Simulations and Diversity Selection by Extended Continuous Similarity Indices

“…This algorithm improves upon our Max_nDis picker 21 because step 2.1 allows for a more thorough selection of the diverse conformations by effectively serving as a tiebreaker between conformations with the same extended similarity with respect to the preselected set. That is, we still use the minimization of the extended similarity (step 2) as the driving force of the algorithm, but step 2.1 adds an extra layer that leads to an even more diverse set in the end.…”

“…The algorithm is inspired by the diversity pickers commonly applied in cheminformatics to sample large chemical spaces, usually based on the use of binary molecular fingerprints. 18 The various versions of the extended similarity indices 18 − 20 have shown great promise in the problems of diversity selection 21 and exploration of large and various data sets 22 , 23 including complex biological ensembles. 24 The keys to this success are the ability of the extended indices to quantify similarities between any number of objects and the fact that they can do so with linear scaling.…”

Chemoinformatics and Artificial Intelligence Colloquium: Progress and Challenges to Develop Bioactive Compounds

“…Extended similarity analysis: from pair of molecules, to chemical space and beyond [22,23] Jürgen Bajorath University of Bonn (Germany)…”