Gaussian Mixture Model (GMM) with MATLAB Implementation

In this article, we provide an in-depth exploration of MATLAB source code for Gaussian Mixture Model (GMM) implementation. GMM serves as a powerful statistical tool widely applied in image processing, speech recognition, machine learning, and various data analysis domains. The model operates by combining multiple Gaussian distributions, whose parameters are estimated using the Expectation-Maximization (EM) algorithm. Our MATLAB implementation demonstrates the complete EM algorithm workflow for GMM parameter estimation, including initialization strategies for mean vectors and covariance matrices. The code structure includes separate functions for expectation steps (calculating posterior probabilities) and maximization steps (updating parameters). We illustrate practical applications for classification and clustering tasks, showing how to compute component responsibilities and assign data points to mixture components. Additionally, we examine techniques for improving model performance through parameter tuning, such as regularization of covariance matrices to prevent singularities. The implementation incorporates cross-validation methods for model accuracy assessment, featuring code for splitting datasets and evaluating log-likelihood scores. The MATLAB source code provides valuable insights into GMM theory and practical implementation, serving as an educational resource for understanding probabilistic modeling techniques.