Multivariate response and parsimony for Gaussian cluster-weighted models

TL;DR

This paper introduces a family of parsimonious Gaussian cluster-weighted models that extend to multivariate responses, capturing correlations and improving clustering performance through eigen-decomposition constraints and an EM algorithm.

Contribution

It proposes a novel multivariate extension of Gaussian cluster-weighted models with eigen-decomposition constraints, providing identifiability conditions and an EM algorithm for improved clustering.

Findings

Model performs well on synthetic and real data

Accounting for linear dependencies enhances clustering accuracy

Outperforms some existing clustering approaches

Abstract

A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate responses. Parsimony is attained by constraining parts of an eigen-decomposition imposed on the component covariance matrices. A sufficient condition for identifiability is provided and an expectation-maximization algorithm is presented for parameter estimation. Model performance is investigated on both synthetic and classical real data sets and compared with some popular approaches. Finally, accounting for linear dependencies in the presence of a linear regression structure is shown to offer better performance, vis-\`{a}-vis clustering, over existing methodologies.