Title: Model-based Clustering with Sparse Covariance Matrices,
Abstract: Finite Gaussian mixture models are widely used for model-based clustering of
continuous data. Nevertheless, since the number of model parameters scales
quadratically with the number of variables, these models can be easily
over-parameterized. For this reason, 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. Model
estimation is carried out using a structural-EM algorithm for parameters and
graph structure estimation, where two alternative strategies based on a genetic
algorithm and an efficient stepwise search are proposed for inference. 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
show that the method attains good classification performance and model quality.