Methods for Merging, Parsimony and Interpretability of Finite Mixture Models

Abstract

To combat the increasing data dimensionality, parsimonious modelling for finite mixture models has risen to be an active research area. These modelling frameworks offer various constraints that can reduce the number of free parameters in a finite mixture model. However, the constraint selection process is not always clear to the user. Moreover, the relationship between the chosen constraint and the data set is often left unexplained. Such issues affect adversely the interpretability of the fitted model. That is, one may end up with a model with reduced number of free parameters, but how it was selected, and what the parameter-reducing constraints mean, remain mysterious. Over-estimation of the mixture component count is another way in which the model interpretability may suffer. When the individual components of a mixture model fail to capture adequately the underlying clusters of a data set, the model may compensate by introducing extra components, thereby representing a single cluster with multiple components. This reality challenges the common assumption that a single component represents a cluster. Addressing the interpretability-related issues can improve the informativeness of model-based clustering, thereby better assisting the user during the exploratory analysis and/or data segmentation step.