Advances in Robust Constrained Model Based Clustering

Abstract

Model-based approaches to cluster analysis and mixture modelling often involve maximizing classification and mixture likelihoods. Robust clustering and mixture modelling procedures, that can resist certain amount of contaminating data, can be introduced by considering trimmed versions of those classification and mixture likelihoods. Without appropriate constrains on the scatter matrices of the components, these trimmed likelihood maximizations result in ill-posed problems. Moreover, non-interesting or “spurious” clusters are often detected by unconstrained algorithms aimed at maximizing these trimmed likelihood criteria.

A useful approach to avoid spurious solutions is to restrict relative components scatter by prespecified tuning constants. Recently new methodologies for constrained parsimonious model-based clustering have been introduced which include, in the untrimmed case, the 14 parsimonious models that are often applied in model-based clustering when assuming normal components as limit cases. In this paper we extend this approach to cope with the presence of atypical observations and discuss two viable strategies for automatically estimating the restriction parameters.