Robust estimation for mixtures of Gaussian factor analyzers, based on trimming and constraints

TL;DR

This paper introduces a robust estimation method for Gaussian factor analyzers that combines covariance restrictions and trimming to improve model reliability and robustness against outliers and spurious solutions.

Contribution

It proposes a novel approach integrating restrictions and trimming with an AECM algorithm for more reliable Gaussian mixture modeling.

Findings

Effective in reducing spurious solutions

Robust against outliers and non-normal data

Demonstrated on AIS dataset with positive results

Abstract

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and the disturbing effects of outlying observations, along maximum likelihood estimation, open serious issues. In this paper we consider restrictions for the component covariances, to avoid spurious solutions, and trimming, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology.