Algorithme EM régularisé
This work addresses a specific issue in clustering for scenarios with limited data, representing an incremental improvement to the EM algorithm.
The paper tackles the problem of singular or poorly conditioned covariance matrices in Gaussian Mixture Models when sample size is smaller than data dimension, resulting in a regularized EM algorithm that shows good performance in clustering experiments on real data.
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