A0207
Title: Parsimonious mixtures of dimension-wise scaled normal mixtures
Authors: Luca Bagnato - Catholic University of the Sacred Heart (Italy) [presenting]
Antonio Punzo - University of Catania (Italy)
Salvatore Daniele Tomarchio - University of Catania (Italy)
Abstract: A new family of parsimonious mixture models is introduced for model-based clustering. Dimension-wise scaled normal mixtures (DSNMs), recently introduced in the literature, are considered as mixture components. DSNMs generalize the multivariate normal (MN) distribution in two directions. Firstly, they have a more general type of symmetry with respect to the elliptical symmetry of the MN distribution. Secondly, the univariate marginals have similar heavy-tailed normal scale mixture distributions with (possibly) different tailedness parameters; as a consequence of practical interest, DSNMs allow for a different excess kurtosis on each dimension. Due to the structure of these mixture components, parsimony is attained through the variance-correlation decomposition. A variant of the expectation-maximization algorithm is presented for maximum likelihood parameter estimation. Parameter recovery and clustering performance are investigated via a simulation study. Comparisons with the unconstrained mixture models are obtained as by-products. Lastly, our and the competing models are evaluated in terms of fitting and clustering on some real datasets.
