Distance phenomena in high-dimensional chemical descriptor spaces: consequences for similarity-based approaches

Measuring the (dis)similarity of molecules is, besides descriptor selection, an important factor for many cheminformatics applications like compound ranking, clustering, and, property prediction. In this work, we focus on real-valued vector spaces (as opposed to the binary spaces of, e.g., fingerprints). We demonstrate the severe influence the choice of (dis)similarity measure can have on the results of cheminformatics applications, and provide recommendations for such choices.

We briefly review the mathematical concepts [1] used to measure (dis)similarity in vector spaces, namely norms, metrics, inner products and similarity coefficients, and the relationships between them, employing commonly used [2][3] (dis)similarity measures in cheminformatics as examples.

Then, we present several phenomena (empty space phenomenon, sphere volume related phenomena, distance concentration [4][5][6]) in high-dimensional descriptor spaces which are not encountered in two and three dimensions. These phenomena are theoretically characterized and illustrated with both artificial and real (bioactivity) data examples.