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Statistical methodology is proposed for comparing unlabeled marked pointsets, with an application to aligning steroid molecules in chemoinformatics.Methods from statistical shape analysis are combined with techniques forpredicting random fields in spatial statistics in order to define a suitablemeasure of similarity between two marked point sets. Bayesian modeling of thepredicted field overlap between pairs of point sets is proposed, and posteriorinference of the alignment is carried out using Markov chain Monte Carlosimulation. By representing the fields in reproducing kernel Hilbert spaces,the degree of overlap can be computed without expensive numerical integration.Superimposing entire fields rather than the configuration matrices of pointcoordinates thereby avoids the problem that there is usually no clearone-to-one correspondence between the points. In addition, mask parameters areintroduced in the model, so that partial matching of the marked point sets canbe carried out. We also propose an adaptation of the generalized Procrustesanalysis algorithm for the simultaneous alignment of multiple point sets. Themethodology is illustrated with a simulation study and then applied to a dataset of 31 steroid molecules, where the relationship between shape and bindingactivity to the corticosteroid binding globulin receptor is explored.

Bayesian matching of unlabeled marked point sets using random fields, with an application to molecular alignment