Gaussian Mixture Model Parameter Estimation with EM Algorithm Implementation

This article provides a detailed explanation of the parameter estimation process for Gaussian Mixture Models (GMM) using the Expectation-Maximization (EM) algorithm. For readers unfamiliar with EM, I'll begin with a brief introduction. The EM algorithm is a classical iterative method used to estimate parameters of probabilistic models from observed data. In this implementation, we focus on Gaussian Mixture Models, which represent complex multivariate distributions as combinations of simpler Gaussian distributions.

To implement GMM parameter estimation, I developed the sunMOG.m function that computationally implements the EM algorithm. The function handles critical operations including initialization of mixture components, E-step calculations for posterior probabilities, and M-step updates for means, covariances, and mixing coefficients. Additionally, I created testMOG4.m as a testing program that validates the function's performance through synthetic data generation, convergence monitoring, and accuracy assessment against ground truth parameters.

This article will thoroughly examine the implementation details of sunMOG.m, explaining how it executes the EM algorithm's iterative process for GMM parameter estimation. I will demonstrate how testMOG4.m evaluates the function's performance through comprehensive testing scenarios. By studying this material, you will gain deeper insights into GMM parameter estimation and learn practical code implementation techniques for statistical modeling.