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

翻译：期望最大化（EM）算法是一种广泛使用的迭代算法，用于在高斯混合模型（GMM）中计算最大似然估计。当样本量小于数据维度时，可能导致协方差矩阵奇异或病态，从而降低性能。本文提出了一种正则化版本的EM算法，该算法有效利用先验知识以应对小样本量问题。该方法旨在最大化带惩罚项的GMM似然函数，其中正则化估计通过将估计量向某些结构化目标协方差矩阵收缩，确保协方差矩阵更新的正定性。最终，真实数据上的实验表明，所提算法在聚类任务中具有良好的性能。