Gaussian Mixture Model Fitting with Parsimonious Clustering of Covariance Matrices.

D. Rodríguez Vítores, C. Matrán Bea

This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of groupings of the 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. Our approach leads to propose Gaussian Mixture Models for model-based clustering and discriminant analysis with 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.

Keywords: Parsimonious model, Gaussian mixture model, Bayesian Information Criterion, Model-based classification.

GT03.AMC4 Clustering and Classification
November 9, 2023  3:30 PM
CC3: Room 1

D. Peña

E. Boj del Val, A. Grané

A. Mayo-Iscar, L. Á. García-Escudero, C. Hennig, G. Morelli, M. Riani