Volume 3 Supplement 1
Distance phenomena in high-dimensional chemical descriptor spaces: consequences for similarity-based approaches
© Rupp and Schneider; licensee BioMed Central Ltd. 2009
Published: 05 June 2009
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  used to measure (dis)similarity in vector spaces, namely norms, metrics, inner products and similarity coefficients, and the relationships between them, employing commonly used  (dis)similarity measures in cheminformatics as examples.
Then, we present several phenomena (empty space phenomenon, sphere volume related phenomena, distance concentration ) 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.
- Meyer C: Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia. 2001Google Scholar
- Leach A, Gillet V: An Introduction to Chemoinformatics. 2003, Springer NetherlandsGoogle Scholar
- Willett P: J Chem Inf Comput Sci. 1998, 38: 983-996.View ArticleGoogle Scholar
- Aggarwal C, Hinneburg A, Keim D: ICDT 2001 Proceedings, 2001, LNCS. 1973, 420-434.Google Scholar
- Beyer K, Goldstein J, Ramakrishnan R, Shaft U: ICDT 1999 Proceedings, LNCS 1540. 1999, 217-235.Google Scholar
- Francois D, Wertz V, Verleysen M: IEEE Trans Knowl Data Eng. 2007, 19: 873-886. 10.1109/TKDE.2007.1037.View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd.