Matrix Normal Cluster-Weighted Models

TL;DR

This paper extends cluster-weighted models to matrix data using matrix normal distributions, enabling more accurate clustering of multivariate data observed over time or space, with applications in education and insurance.

Contribution

It introduces a matrix normal cluster-weighted model with an ECM algorithm for parameter estimation, advancing model-based clustering for matrix-variate data.

Findings

Effective parameter recovery demonstrated on simulated data

Accurate classification performance observed

BIC successfully detects underlying groups

Abstract

Finite mixtures of regressions with fixed covariates are a commonly used model-based clustering methodology to deal with regression data. However, they assume assignment independence, i.e. the allocation of data points to the clusters is made independently of the distribution of the covariates. In order to take into account the latter aspect, finite mixtures of regressions with random covariates, also known as cluster-weighted models (CWMs), have been proposed in the univariate and multivariate literature. In this paper, the CWM is extended to matrix data, e.g. those data where a set of variables are simultaneously observed at different time points or locations. Specifically, the cluster-specific marginal distribution of the covariates, and the cluster-specific conditional distribution of the responses given the covariates, are assumed to be matrix normal. Maximum likelihood parameter estimates are derived using an ECM algorithm. Parameter recovery, classification assessment and the capability of the BIC to detect the underlying groups are analyzed on simulated data. Finally, two real data applications concerning educational indicators and the Italian non-life insurance market are presented.