MATLAB Implementation of EM Algorithm for Clustering Analysis

The Expectation-Maximization (EM) algorithm can be implemented using MATLAB programming language to perform clustering analysis. EM algorithm is an iterative statistical method used for estimating parameters in probabilistic models containing latent variables. In clustering applications, the EM algorithm enables data partitioning into distinct groups based on feature characteristics, facilitating better understanding and interpretation of data structures and patterns.

Key implementation aspects include: Using MATLAB's statistical and machine learning toolbox functions such as fitgmdist for Gaussian Mixture Model fitting, which internally implements the EM algorithm. The algorithm alternates between two main steps: Expectation step (E-step) computes the probability of each data point belonging to each cluster using current parameter estimates, while Maximization step (M-step) updates model parameters by maximizing the expected log-likelihood. Implementation typically involves initializing cluster parameters, iterating until convergence criteria are met, and handling covariance matrix regularization to ensure numerical stability.

For custom implementation, developers can create functions that calculate posterior probabilities, update mean vectors and covariance matrices, and monitor log-likelihood changes. The algorithm effectively handles missing data and provides probabilistic cluster assignments, making it superior to hard-clustering methods like k-means for certain applications.