Model-based Clustering with Sparse Covariance Matrices
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Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, they can suffer of over parameterization. Thus, parsimonious models have been developed via covariance matrix decompositions or assuming local independence. However, these remedies do not allow for direct estimation of sparse covariance matrices nor do they take into account that the structure of association among the variables can vary from one cluster to the other. To this end, we introduce mixtures of Gaussian covariance graph models for model-based clustering with sparse covariance matrices. A penalized likelihood approach is employed for estimation and a general penalty term on the graph configurations can be used to induce different levels of sparsity and incorporate prior knowledge. Optimization is carried out using a genetic algorithm in conjunction with a structural-EM algorithm for parameters and graph structure estimation. With this approach, sparse component covariance matrices are directly obtained. The framework results in a parsimonious model-based clustering of the data via a flexible model for the within-group joint distribution of the variables. Extensive simulated data experiments and application to illustrative datasets shows that the proposed method attains good classification performance and model quality.
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