MM Algorithm for Gaussian Mixture Model Parameter Estimation

The MM algorithm is a widely used method for solving Gaussian Mixture Model (GMM) parameter estimation problems. In this context, the objective is to estimate GMM parameters—including mean vectors, covariance matrices, and mixture coefficients—from given data samples. The algorithm achieves this through iterative parameter optimization using the Expectation-Maximization (EM) framework. The implementation alternates between two key steps: the E-step computes the expected values of latent variables (responsibilities) for each component given the current parameters, while the M-step maximizes the likelihood function to update parameter estimates. The MATLAB source code provides a clear implementation of this EM optimization process, featuring unencrypted, accessible code that allows direct examination and utilization. Key functions include responsibility calculation using multivariate normal distributions, parameter update equations derived from maximum likelihood estimation, and convergence checking mechanisms for iterative refinement.