MATLAB Implementation of EM Algorithm with Code Examples

In this article, we explore the application of the EM (Expectation-Maximization) algorithm in probabilistic statistics and provide executable sample code for MATLAB environments. The EM algorithm is an iterative method for parameter estimation in probabilistic models with broad applications across data analysis domains. Through this algorithm, we can solve complex data analysis challenges such as clustering analysis and classification problems. The accompanying MATLAB implementation demonstrates a practical EM algorithm application for clustering analysis on a sample dataset, featuring key components including: - E-step (Expectation): Computes posterior probabilities using current parameter estimates - M-step (Maximization): Updates parameters by maximizing expected log-likelihood - Convergence checking: Monitors log-likelihood changes between iterations The code structure includes initialization routines, iterative EM loops, and visualization functions for result analysis. To execute, simply extract the package and run the main script in MATLAB. This example provides foundational understanding for extending EM algorithm to more complex statistical models and real-world datasets.