Algorithme EM r\'egularis\'e

TL;DR

This paper introduces a regularized EM algorithm for Gaussian Mixture Models that improves covariance matrix estimation in small sample scenarios by incorporating prior knowledge, leading to better clustering results.

Contribution

It proposes a novel regularized EM algorithm that ensures positive definite covariance matrices using prior information, enhancing performance with limited data.

Findings

Improved covariance matrix estimation in small samples.

Enhanced clustering accuracy on real datasets.

Robustness against ill-conditioned matrices.

Abstract

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing maximum likelihood estimate when dealing with Gaussian Mixture Model (GMM). When the sample size is smaller than the data dimension, this could lead to a singular or poorly conditioned covariance matrix and, thus, to performance reduction. This paper presents a regularized version of the EM algorithm that efficiently uses prior knowledge to cope with a small sample size. This method aims to maximize a penalized GMM likelihood where regularized estimation may ensure positive definiteness of covariance matrix updates by shrinking the estimators towards some structured target covariance matrices. Finally, experiments on real data highlight the good performance of the proposed algorithm for clustering purposes