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Robust clustering of high-dimensional data is an important topic because, inmany practical situations, real data sets are heavy-tailed and/or asymmetric.Moreover, traditional model-based clustering often fails for high dimensionaldata due to the number of free covariance parameters. A parametrization of thecomponent scale matrices for the mixture of generalized hyperbolicdistributions is proposed by including a penalty term in the likelihoodconstraining the parameters resulting in a flexible model for high dimensionaldata and a meaningful interpretation. An analytically feasible EM algorithm isdeveloped by placing a gamma-Lasso penalty constraining the concentrationmatrix. The proposed methodology is investigated through simulation studies andtwo real data sets.

Flexible Clustering with a Sparse Mixture of Generalized Hyperbolic Distributions