Unsupervised Gaussian Mixture Model (GMM) Estimation via EM Algorithm

Unsupervised Gaussian Mixture Model (GMM) estimation via the Expectation-Maximization algorithm represents a fundamental statistical approach for probabilistic clustering. The EM algorithm iteratively performs E-step (computing posterior probabilities using current parameters) and M-step (updating mean vectors, covariance matrices, and mixing coefficients through maximum likelihood estimation) to optimize model parameters. This methodology enables effective data clustering and classification by modeling complex distributions as weighted combinations of Gaussian components. We reference source code from two IEEE papers that demonstrate practical implementations including key functions for handling singular covariance matrices through regularization techniques and implementing convergence criteria based on log-likelihood thresholds. Studying these implementations provides researchers with insights into initialization strategies using k-means clustering and Bayesian information criterion (BIC) for model selection. Further exploration of these resources facilitates advancement in GMM applications across pattern recognition and density estimation domains.