Parameter Estimation Method for Gaussian Mixture Models Using EM Algorithm

This document presents a parameter estimation method for Gaussian Mixture Models based on the Expectation-Maximization (EM) algorithm. The implementation is developed in MATLAB, where the code structure follows the standard EM framework: an initialization phase for mean vectors and covariance matrices, followed by iterative E-steps (computing posterior probabilities using Bayesian inference) and M-steps (updating parameters through maximum likelihood estimation). The algorithm's efficiency stems from its convergence properties, enabling accurate parameter estimation even with large datasets through optimized matrix operations and probability density calculations. This method proves particularly valuable for statistical data analysis applications, offering practical solutions for clustering, density estimation, and pattern recognition problems across various domains. The implementation includes validation checks for covariance matrix conditioning and convergence criteria monitoring to ensure numerical stability.