Irina Czogiel

Dept. of Mathematics and Statistics, Visiting Scholar

University of Nottingham


Bayesian Alignment of Unlabelled Marked Point Sets (Molecular Shape Analysis)

We propose a statistical model for evaluating and comparing molecular shapes. Molecular data are usually given in form of atomic coordinates and some values of molecular properties (e.g. partial charge values) which have been observed at these coordinates. In most data sets, there is no clear correspondence between atoms of different molecules. From a methodological point of view, the task of comparing molecular shapes is therefore that of comparing unlabelled marked point sets.

Methods from statistical shape analysis serve as basis for our model. To account for the continuous nature of molecules, we combine these methods with techniques used for predicting random fields in spatial statistics. In particular, we use kriging to predict the measured values of the considered molecular properties in three--dimensional space. Applying a modification of the ordinary partial Procrustes analysis, we then use an adapted least-squares criterion and Bayesian inference (MCMC) for the pairwise alignment of the resulting molecular fields. Superimposing entire fields rather than the configuration matrices of atomic positions thereby solves the labeling problem, and by incorporating mask parameters in the MCMC procedure we can also account for the fact that only parts of the molecular structures may be similar.

As a further step, we also propose an adaption of the generalized Procrustes analysis algorithm for the simultaneous alignment of molecular fields.


Back to Colloquium Series