A0369
Title: Mixture of matrix-variate normals with mean restrictions
Authors: Marco Berrettini - University of Bologna (Italy) [presenting]
Giuliano Galimberti - University of Bologna (Italy)
Cinzia Viroli - University of Bologna (Italy)
Abstract: Novel strategies are introduced for modeling mean structures in matrix-variate normal distributions, aiming to overcome the common issue of over-parameterization in model-based clustering. The proposed approach relies on parsimonious parameterizations, based on additive components, interaction effects, and low-degree polynomial terms, to effectively capture the intricate multivariate relationships encoded in the mean structure of the data. Particular attention is given to identifiability, and explicit expressions for maximum likelihood estimation under the proposed constraints are derived. To extend these ideas within a clustering framework, finite mixtures of mean-restricted matrix normal distributions are considered, combined with structured covariance matrices that preserve flexibility while reducing the risk of overfitting. An expectation-maximization (EM) algorithm is developed to perform parameter estimation efficiently and reliably. The effectiveness of the proposed methodology is demonstrated through an illustrative application to climate data, where it shows significant improvements over more conventional approaches in detecting meaningful patterns and group structures in high-dimensional, matrix-valued observations.
