A LASSO-Penalized BIC for Mixture Model Selection

A model-based clustering approach assumes that each component or some combination of components corresponds to a cluster. When fitting the model in (1), the main task is to decide the number of components G. Titterington et al. (1985), McLachan and Basford (1988) and McLachan and Peel (2002) extensively reviewed mixture models, with a focus on Gaussian mixture models. Fraley and Raftery (2002) presented a review of work on Gaussian mixtures with a focus on clustering, discriminant analysis, and density estimation. They discuss a family of Gaussian mixture models, which arises from the imposition of constraints upon an eigen-decomposition of the component covariance structure. The family of mixture models they discuss, known as MCLUST, is actually a subset of the Gaussian parsimonious clustering models (GPCMs) of Celeux and Govaert (1995). When using the MCLUST models, one must choose the appropriate member of the family, i.e., the covariance structure, in addition to deciding the number of components G. Ghahramani and Hinton (1997) introduced a mixture of factor analyzers model, which was further developed by Tipping and Bishop (1999) and McLachlan and Peel (2000).