Three-way data clustering based on the mean-mixture of matrix-variate normal distributions

With the steady growth of computer technologies, the application of statistical techniques to analyze extensive datasets has garnered substantial attention. The analysis of three-way (matrix-variate) data has emerged as a burgeoning field that has inspired statisticians in recent years to develop novel analytical methods. This paper introduces a unified finite mixture model that relies on the mean-mixture of matrix-variate normal distributions. The strength of our proposed model lies in its capability to capture and cluster a wide range of three-way data that exhibit heterogeneous, asymmetric and leptokurtic features. A computationally feasible ECME algorithm is developed to compute the maximum likelihood (ML) estimates. Numerous simulation studies are conducted to investigate the asymptotic properties of the ML estimators, validate the effectiveness of the Bayesian information criterion in selecting the appropriate model, and assess the classification ability in presence of contaminated noise. The utility of the proposed methodology is demonstrated by analyzing a real-life data example.