Robust cluster analysis via mixtures of multivariate t-distributions

The expectation-maximization (EM) algorithm can be used to fit mixtures of multivariate t-distributions by maximum likelihood and it is demonstrated how the use of t-components provides less extreme estimates of the posterior probabilities of cluster membership.

Abstract

Normal mixture models are being increasingly used as a way of clustering sets of continuous multivariate data. They provide a probabilistic (soft) clustering of the data in terms of their fitted posterior probabilities of membership of the mixture components corresponding to the clusters. An outright (hard) clustering can be subsequently obtained by assigning each observation to the component to which it has the highest fitted posterior probability of belonging. However, outliers in the data can affect the estimates of the parameters in the normal component densities, and hence the implied clustering. A more robust approach is to fit mixtures of multivariate t-distributions, which have longer tails than the normal components. The expectation-maximization (EM) algorithm can be used to fit mixtures of t-distributions by maximum likelihood. The application of this model to provide a robust approach to clustering is illustrated on a real data set. It is demonstrated how the use of t-components provides less extreme estimates of the posterior probabilities of cluster membership.