Model-based clustering via skewed matrix-variate cluster-weighted models

TL;DR

This paper introduces a flexible family of skewed matrix-variate cluster-weighted models that improve clustering performance on data with skewness or deviations from normality, using an expectation-conditional maximization algorithm.

Contribution

It proposes 24 new matrix-variate CWMs incorporating skewed distributions, enhancing modeling of non-normal data in clustering contexts.

Findings

Parameter recovery and classification are effective in simulations.

BIC successfully detects the true number of clusters.

Models perform well on real datasets.

Abstract

Cluster-weighted models (CWMs) extend finite mixtures of regressions (FMRs) in order to allow the distribution of covariates to contribute to the clustering process. In a matrix-variate framework, the matrix-variate normal CWM has been recently introduced. However, problems may be encountered when data exhibit skewness or other deviations from normality in the responses, covariates or both. Thus, we introduce a family of 24 matrix-variate CWMs which are obtained by allowing both the responses and covariates to be modelled by using one of four existing skewed matrix-variate distributions or the matrix-variate normal distribution. Endowed with a greater flexibility, our matrix-variate CWMs are able to handle this kind of data in a more suitable manner. As a by-product, the four skewed matrix-variate FMRs are also introduced. Maximum likelihood parameter estimates are derived using an expectation-conditional maximization algorithm. Parameter recovery, classification assessment, and the capability of the Bayesian information criterion to detect the underlying groups are investigated using simulated data. Lastly, our matrix-variate CWMs, along with the matrix-variate normal CWM and matrix-variate FMRs, are applied to two real datasets for illustrative purposes.