On Expectation-Maximization Algorithm with Split and Merge in R

Abstract

This paper presents a comprehensive study on the implementation of the Expectation-Maximization (EM) algorithm for a 4-component bivariate Gaussian Mixture Model (GMM) with a focus on incorporating the split and merge techniques. The bivariate GMM is widely utilized in various fields, such as pattern recognition, image processing, and data clustering, due to its flexibility in capturing complex data distributions. Our proposed implementation leverages the versatility of the R programming language to create a robust and efficient framework for modeling and optimizing the parameters of the 4-component GMM. The EM algorithm is employed as a powerful tool for iteratively estimating the model parameters, ensuring convergence to a local maximum of the likelihood function. To enhance the model’s flexibility, we introduce the split and merge strategies, enabling the algorithm to adapt to diverse data structures and efficiently manage the complexity of the mixture components. The split operation allows for the subdivision of components when needed, while the merge operation facilitates the combination of components that represent similar patterns. This adaptive approach contributes to the model’s ability to capture intricate data patterns and improve convergence during the optimization process. The implementation is validated through extensive experimentation on synthetic, demonstrating its effectiveness in accurately estimating the parameters of the 4-component bivariate GMM. The proposed methodology proves to be a valuable addition to the existing tools available for GMM based modeling, providing researchers and practitioners with a flexible and powerful framework for analyzing complex data structures in diverse applications