Gaussian Parsimonious Clustering Models with Covariates and a Noise Component

TL;DR

This paper introduces MoEClust, a suite of Gaussian mixture models that incorporate covariates and noise components, improving clustering accuracy for correlated data with external information.

Contribution

It presents a novel framework combining covariate effects and parsimonious covariance structures in Gaussian mixture models, including noise components and enhanced initialization methods.

Findings

Significant improvement in clustering accuracy with covariate integration.

Effective modeling of outliers using a noise component.

Enhanced model selection and visualization techniques.

Abstract

We consider model-based clustering methods for continuous, correlated data that account for external information available in the presence of mixed-type fixed covariates by proposing the MoEClust suite of models. These models allow different subsets of covariates to influence the component weights and/or component densities by modelling the parameters of the mixture as functions of the covariates. A familiar range of constrained eigen-decomposition parameterisations of the component covariance matrices are also accommodated. This paper thus addresses the equivalent aims of including covariates in Gaussian parsimonious clustering models and incorporating parsimonious covariance structures into all special cases of the Gaussian mixture of experts framework. The MoEClust models demonstrate significant improvement from both perspectives in applications to both univariate and multivariate data sets. Novel extensions to include a uniform noise component for capturing outliers and to address initialisation of the EM algorithm, model selection, and the visualisation of results are also proposed.