Introduction to EM Algorithm with MATLAB Demonstration Code

In the following text, I will introduce the Expectation-Maximization (EM) algorithm and provide MATLAB demonstration code applicable to both 1D and multidimensional Gaussian Mixture Models (GMM). The EM algorithm is an iterative method for unsupervised learning, used to estimate parameters in probabilistic models with latent variables. By treating data as consisting of both latent hidden variables and observable variables, the EM algorithm can be employed to find maximum likelihood estimates or maximum a posteriori probability estimates. Gaussian Mixture Models, both 1D and multidimensional, are commonly used models for representing data composed of multiple distinct Gaussian distributions. Through MATLAB demonstrations of these algorithms, you will learn how to implement the EM algorithm for GMM parameter estimation, including essential functions like expectation step calculation (computing posterior probabilities) and maximization step updates (re-estimating means, covariances, and mixing coefficients). This practical implementation will help you understand how to use EM algorithms and Gaussian Mixture Models to analyze and process real-world data sets efficiently.