Abstract

Gaussian mixture models are a standard tool for model-based clustering, but they are often inadequate when clusters exhibit different tail behavior across dimensions. This work presents a new clustering approach based on dimension-wise scaled normal mixtures (DSNMs), a flexible class of multivariate distributions that allows dimension-specific excess kurtosis while preserving the important property that uncorrelated components are independent. We develop parsimonious finite mixtures of DSNMs for clustering symmetric but heterogeneously heavy-tailed data, focusing on mixtures of dimension-wise scaled shifted exponential normal (DSSEN) distributions with closed-form densities. Structured constraints on correlation, scale, and kurtosis parameters lead to a family of interpretable models estimated via an expectation-conditional maximization algorithm. Simulated and real-data examples demonstrate improved robustness and clustering performance compared to existing heavy-tailed mixture models.