Model-based clustering via parsimonious mixtures of dimension-wise scaled normal mixtures

Dimension-wise scaled normal mixtures (DSNMs) are a recently introduced class of continuous multivariate distributions that generalize the multivariate normal distribution by allowing (1) a broader form of central symmetry and (2) dimension-specific excess kurtosis. In this paper, we propose parsimonious finite mixtures of DSNMs for model-based clustering, specifically addressing scenarios with central symmetric clusters that differ in tail heaviness across dimensions. To achieve parsimony, we introduce structured constraints on the correlation, scale, and kurtosis parameters, resulting in a flexible family of 60 interpretable models. We outline expectation-maximization-based algorithms to obtain maximum likelihood estimates. As a concrete example, we focus on mixtures of dimension-wise scaled shifted exponential normal (DSSEN) distributions, a special case of DSNMs having closed-form joint density. Finally, we illustrate the practical advantages of the parsimonious DSSEN mixtures with applications to simulated and real-world data, benchmarking its performance against established mixtures of symmetric heavy-tailed distributions.