Model-based clustering via linear cluster-weighted models

TL;DR

This paper introduces a new family of twelve robust mixture models with covariates for model-based clustering, extending the linear Gaussian CWM to include linear $t$ CWMs, and demonstrates their effectiveness through real data applications and simulations.

Contribution

It proposes a unified family of robust mixture models with covariates, including the linear Gaussian CWM as a special case, and develops an EM-based estimation and model selection framework.

Findings

The models perform well in real data clustering tasks.

BIC and ICL effectively select the appropriate model.

Simulation studies validate the robustness and accuracy of the proposed methods.

Abstract

A novel family of twelve mixture models with random covariates, nested in the linear $t$ cluster-weighted model (CWM), is introduced for model-based clustering. The linear $t$ CWM was recently presented as a robust alternative to the better known linear Gaussian CWM. The proposed family of models provides a unified framework that also includes the linear Gaussian CWM as a special case. Maximum likelihood parameter estimation is carried out within the EM framework, and both the BIC and the ICL are used for model selection. A simple and effective hierarchical random initialization is also proposed for the EM algorithm. The novel model-based clustering technique is illustrated in some applications to real data. Finally, a simulation study for evaluating the performance of the BIC and the ICL is presented.