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.