Model-based cluster analysis using Bayesian techniques

Model-based cluster analysis is a common clustering method. Unlike the classical clustering methods, model-based clustering assumes that the data come from several subpopulations, which can be modeled separately. A finite mixture model is used to describe the overall population. Some basic problems that arise in cluster analysis, such as determination of the number of clusters and choosing an appropriate clustering method for a given problem, can be considered as model selection in the mixture modeling approach. In our study, we model each subpopulation using multivariate normal density. The covariance matrix of each subpopulation in our model is parameterized using spectral decomposition based on Givens rotation matrices. We introduce a covariance structure indicator in our model, which increases the accuracy of estimation. For model selection problem, we introduce a reversible jump MCMC algorithm which uses normal proposal distributions instead of constructing bijections to perform the jumps between parameter spaces of different dimensions