Gaussian Mixture Model (GMM) - MATLAB Implementation with EM Algorithm

This repository provides MATLAB source code for Gaussian Mixture Model (GMM) implementation. Gaussian Mixture Model (GMM) is a probabilistic model that describes data sets composed of multiple Gaussian distributions. It is commonly used for clustering and density estimation tasks. Using GMM, data sets can be decomposed into multiple Gaussian components, providing better understanding of the underlying data structure. In MATLAB, we implement the Expectation-Maximization (EM) algorithm to fit GMM parameters, which involves two iterative steps: E-step (computing posterior probabilities) and M-step (updating Gaussian parameters). This trained model can then be used for classification and clustering applications. When implementing GMM, we need to specify the number of Gaussian components and initial parameters. If too few components are selected, the model may become oversimplified and fail to capture data complexity. Conversely, selecting too many components may lead to overfitting and performance degradation. Therefore, careful parameter tuning using techniques like cross-validation or information criteria (AIC/BIC) is essential for optimal component selection. The MATLAB implementation includes key functions such as gmdistribution.fit() (or fitgmdist in newer versions) for model training, which handles covariance matrix types (full, diagonal, spherical) and regularization options. Additional utility functions support probability density calculation, component responsibility assignment, and model visualization. In summary, GMM is a powerful probabilistic model applicable to various machine learning tasks. The MATLAB implementation using EM algorithm provides an efficient way to fit GMM models for classification and clustering applications. This source code serves as a practical reference for understanding and applying Gaussian mixture models in real-world scenarios.