EM Algorithm for Gaussian Mixture Models (GMM) with MATLAB Implementation

In this article, we explore the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) and provide its implementation in MATLAB. The EM algorithm is an iterative method used for estimating unknown parameters in mixture models, widely applied in various fields including image processing, speech recognition, and bioinformatics. Our implementation includes key MATLAB functions for handling parameter initialization, E-step (computing posterior probabilities using Bayes' theorem), and M-step (updating means, covariances, and mixing coefficients through maximum likelihood estimation). We provide detailed discussions on the algorithm's core principles, including log-likelihood computation, convergence criteria, and covariance regularization techniques to prevent singular matrix issues. The code structure demonstrates proper handling of multidimensional data and includes visualization components for analyzing clustering results. This article aims to offer valuable insights and practical assistance for understanding and applying this powerful statistical modeling technique.