Parsimonious skew mixture models for model-based clustering and classification

Robust mixture modeling approaches using skewed distributions have recently been explored to accommodate asymmetric data. Parsimonious skew-t and skew-normal analogues of the GPCM family that employ an eigenvalue decomposition of a scale matrix are introduced. The methods are compared to existing models in both unsupervised and semi-supervised classification frameworks. Parameter estimation is carried out using the expectation-maximization algorithm and models are selected using the Bayesian information criterion. The efficacy of these extensions is illustrated on simulated and real data sets.