To note, one major train of thought for cutting down on computation times began with the introduction of the modal fingerprint. Methods to speed up these routine calculations are therefore sought after. While this is fine up until a certain size, the similarity matrix calculation scales quadratically with the number of molecules, O( N 2), resulting in very long computation times for larger sets. Likewise, popular diversity selection algorithms require pre-calculating the full similarity matrix of the compound pool. Ĭlassically, we can estimate the diversity of a compound set with binary comparisons by calculating its full similarity matrix. It is also worth noting that Tanimoto and other metrics can also be applied to quantify field-based representations, like shape similarity. We have also dedicated a paper to develop an efficient mathematical framework to study the consistency of arbitrary similarity metrics. In our earlier investigations we could prove the equivalency of several coefficients, as well as identify a few alternatives to the popular Tanimoto similarity. 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”. have also called for attention that the “widely and almost exclusively applied Tanimoto similarity coefficient has deficiencies together with the Daylight fingerprints”. He also calculated multiple database rankings using a fixed reference structure and the rank positions were concatenated, in a process called “similarity fusion”. 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”. It is well- known that “the results of similarity assessment vary depending on the compound representation and metric”. Generally, binary fingerprints serve to define binary similarity (and distance) coefficients, which are routinely used in virtual screening, fragment-based de novo ligand design, hit-to-lead optimization, etc. However, the quantification of molecular similarity is not a trivial task. Molecular similarity is a key concept in cheminformatics, drug design and related subfields. The Python code for calculating the extended similarity metrics is freely available at: We also present a conceptual example of the applicability of our indices in agglomerative hierarchical algorithms. 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 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 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. Remarkably, for large datasets, the use of extended similarity measures provides an unprecedented speed-up over “traditional” pairwise similarity matrix calculations. 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. Their features were revealed by sum of ranking differences and ANOVA. Part 1 is a detailed analysis of the effects of various parameters on the similarity values calculated by the extended formulas. comparisons of more than two molecules at a time) but defined a series of novel idices. In a recent contribution we have not only introduced a complete mathematical framework for extended similarity calculations, (i.e. 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.
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