Parsimonious skew mixture models for model-based clustering and classification

Abstract

In recent work, robust mixture modelling approaches using skewed distributions have been explored to accommodate asymmetric data. We introduce parsimony by developing skew-t and skew-normal analogues of the popular GPCM family that employ an eigenvalue decomposition of a positive-semidefinite matrix. The methods developed in this paper are compared to existing models in both an unsupervised and semi-supervised classification framework. Parameter estimation is carried out using the expectationmaximization algorithm and models are selected using the Bayesian information criterion. The efficacy of these extensions is illustrated on simulated and benchmark clustering data sets.

Mixture model selection via hierarchical BIC

“…The Matlab software mixmod (Biernacki et al, 2006) and R software mixture (Browne and McNicholas, 2014) implement all of the fourteen models. Recent developments of EDGMM include the incorporation of t distributions to deal with outliers (t-EDGMM; Andrews and McNicholas, 2012), the incorporation of skew distributions to further tackle asymmetry (skew-EDGMM; Vrbik and McNicholas, 2014) and the extension of t-EDGMM in the presence of missing data (Lin, 2014). A central issue in learning EDGMM is to determine a suitable number of mixture components and covariance structure.…”

An alternative classification to mixture modeling for longitudinal counts or binary measures

“…For non-continuous data, either longitudinal or multi-dimensional, the classification is often performed by mixture modeling. [15][16][17][18] In the case of trajectory classification, each individual trajectory is modeled by a mixture of a finite number of polynomials or spline functions, the mixing proportions varying from one individual to another. Some methods assume that there is no intra-group heterogeneity (e.g.…”

Clustering with the multivariate normal inverse Gaussian distribution

“…However this approach still implies that the data are elliptically contoured within each group (Ban eld and Raftery, 1993). To address this issue, mixtures of skew-normal or skew-t distributions can be used (Lin et al, 2007b,a;Cabral et al, 2012;Prates et al, 2013a;Vrbik and McNicholas, 2014). However, these distributions can prove numerically unstable in high-dimensional settings (Fruhwirth-Schnatter and Pyne, 2009).…”