Data Clustering Analysis Using Gaussian Mixture Models

This document presents a comprehensive MATLAB program for performing data clustering analysis using Gaussian Mixture Models (GMM). Gaussian Mixture Model is a widely-used clustering algorithm that partitions datasets into multiple clusters, each modeled as a Gaussian distribution. The implementation leverages MATLAB's Statistics and Machine Learning Toolbox, specifically utilizing the fitgmdist function for model fitting and cluster assignment. The program systematically covers essential workflow steps: data import and preprocessing using readtable or csvread functions, parameter configuration (number of components, covariance type selection), model fitting with expectation-maximization (EM) algorithm optimization, and result visualization through scatter plots and probability density surface plotting. Key implementation aspects include handling covariance matrices via 'full' or 'diagonal' options, determining optimal component numbers using AIC/BIC criteria, and cluster assignment based on posterior probabilities. Through this implementation, users will understand GMM's fundamental principles including probability density estimation and soft clustering approaches, while gaining practical MATLAB skills for performing sophisticated data clustering analysis. The code demonstrates proper handling of convergence criteria, initialization methods, and model validation techniques essential for robust clustering applications.