Implementation of Gaussian Mixture Model Using Expectation Maximization Algorithm

This MATLAB-implemented program leverages the Expectation Maximization (EM) algorithm to compute Gaussian Mixture Models (GMMs). The implementation includes two core phases: the E-step (Expectation) calculates posterior probabilities using Bayes' theorem, while the M-step (Maximization) updates Gaussian parameters (mean, covariance, and mixing coefficients) via maximum likelihood estimation. The program supports versatile data analysis applications, including image processing, signal analysis, and machine learning tasks. It features an intuitive interface allowing users to customize parameters such as the number of Gaussian components, convergence thresholds, and initialization methods (e.g., k-means clustering). Key functions include: - **gmm_em()**: Main function implementing iterative EM optimization with log-likelihood monitoring - **initialize_parameters()**: Handles Gaussian component initialization using random seeding or clustering - **compute_posteriors()**: Calculates component responsibilities using multivariate Gaussian PDFs The package includes detailed documentation and sample scripts demonstrating GMM fitting for multidimensional data, model selection via AIC/BIC criteria, and visualization tools for cluster boundaries and probability densities.