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

Abstract

Quantification of the similarity of objects is a key concept in many areas of computational science. This includes cheminformatics, where molecular similarity is usually quantified based on binary fingerprints. While there is a wide selection of available molecular representations and similarity metrics, there were no previous efforts to extend the computational framework of similarity calculations to the simultaneous comparison of more than two objects (molecules) at the same time. The present study bridges this gap, by introducing a straightforward computational framework for comparing multiple objects at the same time and providing extended formulas for as many similarity metrics as possible. In the binary case (i.e. when comparing two molecules pairwise) these are naturally reduced to their well-known formulas. We provide a detailed analysis on the effects of various parameters on the similarity values calculated by the extended formulas. The extended similarity indices are entirely general and do not depend on the fingerprints used. Two types of variance analysis (ANOVA) help to understand the main features of the indices: (i) ANOVA of mean similarity indices; (ii) ANOVA of sum of ranking differences (SRD). Practical aspects and applications of the extended similarity indices are detailed in the accompanying paper: Miranda-Quintana et al. J Cheminform. 2021. 10.1186/s13321-021-00504-4. Python code for calculating the extended similarity metrics is freely available at: https://github.com/ramirandaq/MultipleComparisons.

Graph-based molecular Pareto optimisation

“…To calculate the diversity of molecules, the pairwise similarity of each combination of molecules in a set has been traditionally calculated using a binary similarity index, like the Tanimoto similarity, 54,55 and summarised in an aggregate metric. However, the recent development of extended similarity metrics 71,72 enables the simultaneous and straightforward comparison of an arbitrary number of bitvectors such as molecular ngerprints.…”

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

“…Additionally, the two novel methods discussed at the meeting: the Extended Similarity Indices [22,23] developed by the research group of Miranda-Quintana, and the Structure-Activity Relationships Matrix (SARM) by the group of Bajorath [25], can be helpful in multiple applications such as analog series identification (fragmentation), de novo drug design signatures study, SAR visualization, reactivity predictions, similarity searching, and visualization of chemical space.…”

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

Molecular dynamics simulations and diversity selection by extended continuous similarity indices

“…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][19][20] have shown great promise in the problems of diversity selection 21 and exploration of large and various datasets 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.…”