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

Ramón Alain Miranda-Quintana,Károly Héberger,Anita Rácz,Dávid Bajusz

doi:10.1186/s13321-021-00504-4

Ramón Alain Miranda-Quintana, Károly Héberger + Show 2 more

Open Access

https://doi.org/10.1186/s13321-021-00504-4

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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 the n-ary and binary indices rank the data in the same way. We demonstrate the use of the new n-ary similarity metrics on t-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

Highlights

Molecular similarity is a key concept in cheminformatics, drug design and related subfields [1, 2]
Willett carried out a detailed comparison of a large number of similarity coefficients and established that the “well-known Tanimoto coefficient remains the method of choice for the computation of fingerprint-based similarity” [13]
If the compounds are selected using an optimal spread design, “the Tanimoto coefficient is intrinsically biased toward smaller compounds, when molecules are described by binary vectors with bits corresponding to the presence or absence of structural features” [16]

Summary

Introduction

Molecular similarity is a key concept in cheminformatics, drug design and related subfields [1, 2]. Miranda‐Quintana et al J Cheminform (2021) 13:33 It is well- known that “the results of similarity assessment vary depending on the compound representation and metric” [10,11,12]. Willett carried out a detailed comparison of a large number of similarity coefficients and established that the “well-known Tanimoto coefficient remains the method of choice for the computation of fingerprint-based similarity” [13]. He calculated multiple database rankings using a fixed reference structure and the rank positions were concatenated, in a process called “similarity fusion” [14]. If the compounds are selected using an optimal spread design, “the Tanimoto coefficient is intrinsically biased toward smaller compounds, when molecules are described by binary vectors with bits corresponding to the presence or absence of structural features” [16]

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