Improving Model Choice in Classification: An Approach Based on Clustering of Covariance Matrices

TL;DR

This paper proposes a clustering-based refinement of Gaussian Mixture Models that groups covariance matrices to improve model interpretability and flexibility in classification and clustering tasks.

Contribution

It introduces a novel approach to cluster covariance matrices within Gaussian Mixtures, creating models with fewer parameters and enhanced interpretability.

Findings

Effective covariance matrix clustering improves model simplicity.

Enhanced models outperform traditional parsimonious models in data fitting.

Applicable to both simulated and real datasets for clustering and discriminant analysis.

Abstract

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters of the involved covariance matrices according to a criterion, such as sharing Principal Directions. This and other similarity criteria that arise from the spectral decomposition of a matrix are the bases of the Parsimonious Model. We show that such groupings of covariance matrices can be achieved through simple modifications of the CEM (Classification Expectation Maximization) algorithm. Our approach leads to propose Gaussian Mixture Models for model-based clustering and discriminant analysis, in which covariance matrices are clustered according to a parsimonious criterion, creating intermediate steps between the fourteen widely known parsimonious models. The added versatility not only allows us to obtain models with fewer parameters for fitting the data, but also provides greater interpretability. We show its usefulness for model-based clustering and discriminant analysis, providing algorithms to find approximate solutions verifying suitable size, shape and orientation constraints, and applying them to both simulation and real data examples.