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Bayesian Alignment of Unlabelled Marked Point Sets Using Random Fields

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In structural bioinformatics and chemoinformatics it is of great interest to align molecules, but the task is often very difficult. Statistical methodology is proposed for comparing unlabelled marked point sets, with an application to aligning steroid molecules in chemoinformatics. Methods from statistical shape analysis are combined with techniques for predicting random fields in spatial statistics in order to define a suitable measure of similarity between two molecules. Bayesian modelling of the predicted field overlap between pairs of molecules is proposed, and posterior inference of the alignment is carried out using Markov chain Monte Carlo simulation. By representing the fields in reproducing kernel Hilbert spaces, the degree of molecule overlap can be computed without expensive numerical integration. Superimposing entire fields rather than the configuration matrices of point co—ordinates thereby avoids the problem that there is usually no clear one—to—one correspondence between the atoms. Using a similar concept, we also propose an adaptation of the generalized Procrustes analysis algorithm for the simultaneous alignment of multiple point sets. The methodology is illustrated with a simulation study and then applied to the dataset of 31 steroid molecules, where the relationship between shape and binding activity to the corticosteroid binding globulin receptor is explored.

This is joint work with Irina Czogiel and Chris Brignell.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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