Molecular similarity measures.

Molecular similarity is a pervasive concept in chemistry. It is essential to many aspects of chemical reasoning and analysis and is perhaps the fundamental assumption underlying medicinal chemistry. Dissimilarity, the complement of similarity, also plays a major role in a growing number of applications of molecular diversity in combinatorial chemistry, high-throughput screening, and related fields. How molecular information is represented, called the representation problem, is important to the type of molecular similarity analysis (MSA) that can be carried out in any given situation. In this work, four types of mathematical structure are used to represent molecular information: sets, graphs, vectors, and functions. Molecular similarity is a pairwise relationship that induces structure into sets of molecules, giving rise to the concept of a chemistry space. Although all three concepts molecular similarity, molecular representation, and chemistry space are treated in this chapter, the emphasis is on molecular similarity measures. Similarity measures, also called similarity coefficients or indices, are functions that map pairs of compatible molecular representations, that is, representations of the same mathematical form, into real numbers usually, but not always, lying on the unit interval. This chapter presents a somewhat pedagogical discussion of many types of molecular similarity measures, their strengths and limitations, and their relationship to one another.