MATLAB Implementation of EM Algorithm for Gaussian Mixture Model Parameter Estimation

This documentation presents a mathematical approach called the Expectation-Maximization (EM) algorithm, implemented in MATLAB for estimating the means, variances, and weights of Gaussian Mixture Models. The EM algorithm operates as an iterative optimization method that progressively approximates maximum likelihood estimates for given data, enabling better understanding of data distribution patterns. Key implementation aspects include: - E-step (Expectation): Computes posterior probabilities using current parameter estimates - M-step (Maximization): Updates parameters by maximizing the expected complete-data log-likelihood - Convergence checking: Implements tolerance-based stopping criteria for iterative refinement In practical applications, this method finds utility across multiple domains including image processing, signal analysis, and natural language processing tasks. The implementation provides a valuable tool for researchers to effectively model and understand distribution characteristics across various data types. The code structure typically involves initialization of GMM parameters, iterative expectation and maximization steps, and convergence validation using likelihood-based metrics.