EM (Expectation Maximization) Algorithm Implementation in MATLAB

This article discusses the EM (Expectation Maximization) algorithm for pattern classification. The EM algorithm is a fundamental machine learning technique that employs probabilistic models to perform classification tasks. The algorithm operates through iterative optimization: during the classification process, it repeatedly computes probability distributions for each class and assigns data points to their most probable categories. This iterative process continues until convergence is achieved. Our implementation utilizes MATLAB, a powerful computational environment ideal for mathematical operations. MATLAB's efficient matrix computation capabilities and built-in functions for statistical analysis make it particularly suitable for implementing the EM algorithm. Key implementation aspects include: - Initialization of Gaussian mixture parameters (means and covariances) - E-step computation using posterior probability calculations - M-step parameter updates through maximum likelihood estimation - Convergence checking based on log-likelihood thresholds The MATLAB implementation enables rapid matrix operations and data visualization, significantly improving efficiency for pattern classification tasks. This allows researchers to obtain accurate classification results faster while maintaining robust probabilistic foundations.