Gaussian Mixture Model Implementation with EM Algorithm

This program is specifically designed to address parameter estimation challenges in Gaussian Mixture Models using the Expectation-Maximization (EM) algorithm. The implementation features modular code architecture where mean estimation, covariance calculation, and weight optimization are developed as standalone functions, each saved as separate .M files for maintainability and reuse. The main.m file serves as the primary execution entry point, coordinating the EM algorithm's iterative E-step (expectation) and M-step (maximization) phases. Prior to execution, users must import sample data into the program environment. The provided sample dataset is stored in spreadsheet format and can be seamlessly loaded using built-in data parsing functions. For customized applications, users may substitute their own datasets while maintaining the required data structure format. We strongly recommend reviewing the source code to understand function interdependencies, algorithmic flow, and parameter initialization procedures. This understanding will facilitate necessary modifications and optimizations, particularly for adjusting convergence criteria, handling covariance singularities, or adapting to different data dimensionalities. The code includes detailed comments explaining key operations such as posterior probability calculations in the E-step and maximum likelihood updates in the M-step.