Alternative weighting schemes for fine-tuned extended similarity indices

Extended similarity indices (i.e., generalization of pairwise similarity) have recently gained importance because of their simplicity, fast computation and superiority in tasks like diversity picking. However, they operate with several meta parameters that should be optimized. Earlier, we extended the binary similarity indices to 'discrete non-binary' and 'continuous' data; now we continue with introducing and comparing multiple weighting functions. As a case study, the similarity of CYP enzyme inhibitors (4016 molecules after curation) was characterized by their extended similarities, based on 2D descriptors, MACCS and Morgan fingerprints. A statistical workflow based on sum of ranking differences (SRD) and analysis of variance (ANOVA) was used for finding the optimal weight function(s). Overall, the best weighting function is the fraction ("frac"), which corresponds to the principle of parsimony. Optimal extended similarity indices were also found, and their differences are revealed across different data sets. We intend this work to be a guideline for users of extended similarity indices regarding the various weighting options available. Source code for the calculations is available at https://github.com/mqcomplab/MultipleComparisons.