A Statistical Perspective on Molecular Similarity

This section will cover tagging of book web only. Although chemists have been using arguments based on molecular similarity to explain and explore chemistry since the days of medieval alchemy, quantitative approaches based on molecular similarity emerged only in the latter half of the twentieth century. The use of quantum mechanical properties and descriptors, typically the electron density, to describe molecular similarity emerged even later, in the 1980s. This chapter reinterprets and revises the framework based on statistical principles. Shepard interpolation is used quite frequently for interpolating points on potential energy surface in chemistry, but it does not seem popular in the molecular similarity field. The boundedness from above ensures that if one considers a case where the unknown molecule is very dissimilar to all the molecules in the training set, the property value predicted by Shepard interpolation approaches the arithmetic mean of the property values of the training data.