Model based clustering using finite mixtures of multivariate geometric skew normal distribution

Abstract

The non-normal distributions for finite mixture model techniques to clustering have been well developed and much used. Particularly, in case of finite mixture models, the component distributions are skewed for multivariate data. It is shown that clustering approach to finite mixture models analyzes the data for asymmetric behavior and heavy tails. In this paper, clustering using multivariate geometric skew normal mixture models has been discussed. The Expectation Maximization (EM) is used to compute maximum likelihood estimates for finite mixture of multivariate geometric skew normal mixture models. Bayesian Information Criterion and Akaike Information Criterion are used for model selection. Eigen value decomposition of covariance matrix are considered and compared to each other. This clustering approach is illustrated with the help of simulated and real life datasets where comparisons are drawn with other mixture models.