Clustering Based on Nonparanormal Graphical Mixture Models

Graphical mixture models provide a powerful tool to visually depict the conditional independence relationships between high-dimensional heterogeneous data. In the study of these models, the distribution of the mixture components is mostly considered multivariate normal with different covariance matrices. The resulting model is known as the Gaussian graphical mixture model. The nonparanormal graphical mixture model has been introduced by replacing the limiting normal assumption with a semiparametric Gaussian copula, which extends the nonparanormal graphical model and mixture models. This study proposes clustering based on the nonparanormal graphical mixture model with two forms of $ell_1$ penalty function (conventional and unconventional), and its performance is compared with the clustering method based on the Gaussian graphical mixture model. The results of the simulation study on normal and nonparanormal datasets in ideal and noisy settings, as well as the application to breast cancer data set, showed that the combination of the nonparanormal graphical mixture model and the penalty term depending on the mixing proportions, both in terms of cluster reconstruction and parameters estimation, is more accurate than the other model-based clustering methods.