🤖 AI Summary
This work addresses the issue of over-parameterization in clustering skewed random matrices by proposing a family of parsimonious mixture models that integrate the skew-t distribution with bilinear factor analysis. This model family systematically encompasses 256 distinct parameter constraint configurations, substantially reducing model complexity while preserving expressive capacity. An AECM algorithm is employed for efficient parameter estimation. Empirical validation on the MNIST and Olivetti face datasets demonstrates that the proposed approach maintains or even enhances clustering performance despite a significant reduction in the number of parameters, thereby achieving a unified framework for dimensionality reduction, robust modeling, and efficient clustering.
📝 Abstract
Mixture models which cluster skewed random matrices can often suffer from over-parameterization in the absence of performing dimension reduction. Even with the use of bilinear factor analyzers, further parameter reduction can be achieved by constraining parameters over clusters. In this manuscript propose a parsimonious family of 256 models for mixtures of skewed matrix variate bilinear factor analyzers, specifically in the case of the skew t distribution. An AECM algorithm for parameter estimation is discussed in detail. Further, extensive simulations are performed, and the method is considered in the case of the MNIST dataset and the Olivetti faces dataset.