Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood
IEEE Transactions on Pattern Analysis and Machine Intelligence
Modelling high-dimensional data by mixtures of factor analyzers
Computational Statistics & Data Analysis
Enhanced Model-Based Clustering, Density Estimation,and Discriminant Analysis Software: MCLUST
Journal of Classification
Generating random correlation matrices based on partial correlations
Journal of Multivariate Analysis
A hierarchical mixture model for clustering three-way data sets
Computational Statistics & Data Analysis
Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches
Journal of Classification
Matrix-Variate Factor Analysis and Its Applications
IEEE Transactions on Neural Networks
On matrix-variate regression analysis
Journal of Multivariate Analysis
Separable linear discriminant analysis
Computational Statistics & Data Analysis
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Matrix-variate distributions represent a natural way for modeling random matrices. Realizations from random matrices are generated by the simultaneous observation of variables in different situations or locations, and are commonly arranged in three-way data structures. Among the matrix-variate distributions, the matrix normal density plays the same pivotal role as the multivariate normal distribution in the family of multivariate distributions. In this work we define and explore finite mixtures of matrix normals. An EM algorithm for the model estimation is developed and some useful properties are demonstrated. We finally show that the proposed mixture model can be a powerful tool for classifying three-way data both in supervised and unsupervised problems. A simulation study and some real examples are presented.