Bayesian Alignment of Unlabeled Marked Point Sets Using Random Fields

Statistical methodology is proposed for comparing unlabeled marked point sets, with an application to aligning 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 modeling 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. In addition mask parameters are introduced in the model, so that partial matching of molecules can be carried out. We also propose an adaptation of the generalized Procrustes analysis algorithm for the simultaneous alignment of multiple point sets. The methodology is 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.

Dr. Ian Dryden

Professor, Department of Statistics, University of South Carolina on April 15, 2011 at 1:00 PM in Engineering Building III, Room 2213

Ian L. Dryden received a Ph.D. degree in statistics from the University of Leeds, UK in 1989. He has been a Professor in the Department of Statistics, University of South Carolina since 2009. Previous positions include Lecturer and Senior Lecturer at the University of Leeds, visiting assistant professor at the University of Chicago, and Professor of Statistics at the University of Nottingham, UK. His research interests include shape analysis, statistical image analysis, medical image analysis, spatial statistics, high-dimensional data analysis, and applications of statistics in biology, medicine and computer science. He was recently chair of the Research Section of the Royal Statistical Society.

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