MATLAB Source Code for Gaussian Mixture EM Algorithm with Three Parameter Estimation

In this article, we will explore the MATLAB source code implementation of the Gaussian Mixture Expectation-Maximization (EM) algorithm. The Gaussian Mixture EM algorithm is a statistical method used for estimating probability density functions from datasets. It can learn multiple components within multivariate Gaussian distributions, where each component maintains its own mean vector and covariance matrix. The algorithm requires estimation of three fundamental parameters: mixture coefficients (representing component weights), mean vectors (defining component centers), and covariance matrices (describing component shapes and orientations). Our MATLAB implementation features iterative expectation and maximization steps, where the E-step computes posterior probabilities using Bayes' theorem, and the M-step updates parameters through maximum likelihood estimation. Key implementation aspects include: - Initialization using k-means clustering for stable parameter starting values - Logarithmic probability computations for numerical stability - Regularization techniques to prevent singular covariance matrices - Convergence checking based on log-likelihood improvement thresholds We will demonstrate this algorithm's practical effectiveness through MATLAB code validation on real-world datasets, showing how it automatically determines optimal Gaussian components while handling complex data distributions. The implementation includes visualization functions to plot resulting Gaussian components over original data points for performance assessment.