MATLAB Implementation of MEL for Estimating GMM Parameters

I would like to share my MATLAB source code for estimating Gaussian Mixture Model (GMM) parameters using Maximum Expected Likelihood (MEL). This code serves as a practical tool for parameter estimation in GMM applications and includes several implementation enhancements for better performance. First, let me explain the core implementation approach. The MEL code primarily utilizes the Expectation-Maximization (EM) algorithm for parameter estimation. This iterative algorithm operates through two main phases repeated until convergence: - E-step (Expectation): Computes the posterior probabilities of each data point belonging to each Gaussian component using current parameter estimates - M-step (Maximization): Updates the Gaussian parameters (means, covariances, and mixing coefficients) based on the computed probabilities The algorithm implementation includes convergence checks using likelihood improvement thresholds and maximum iteration limits to ensure computational efficiency. Each iteration recalculates component responsibilities and updates parameters using weighted averages of the data points. Beyond the basic EM algorithm, I've incorporated several optimization techniques: - Vectorization: Matrix operations replace loops for computational efficiency, particularly in probability calculations and parameter updates - Numerical stability: Logarithmic domain computations prevent underflow in probability calculations, and regularization terms maintain covariance matrix invertibility - Initialization strategies: K-means clustering provides robust initial parameter estimates to avoid poor local optima This MEL implementation supports customizable Gaussian components and includes options for different covariance structures (full, diagonal, or spherical). The code returns complete parameter estimates along with convergence statistics. Overall, this MEL code provides a reliable foundation for GMM parameter estimation with attention to both accuracy and computational performance. For interested users, I can provide additional documentation and usage examples demonstrating application to various datasets and model configurations.