Elliptical Mixture Models Improve the Accuracy of Gaussian Mixture Models with Expectation-maximization Algorithm

This study addresses the limitations of Gaussian Mixture Models (GMMs) in clustering complex datasets and proposes Elliptical Mixture Models (EMMs) as a robust and flexible alternative. By adapting the Expectation-Maximization (EM) algorithm to handle elliptical distributions, the study introduces a novel computational framework that enhances clustering performance for data with irregular shapes and heavy tails. Leveraging the integration of R’s advanced statistical tools into Python workflows, this approach enables practical implementation of EMMs. Empirical evaluations on three datasets Rice, Customer Churn, and Glass Identification demonstrate the superiority of EMMs over GMMs across multiple metrics, including Weighted Average Purity, Dunn Index, Rand Index, and Silhouette Score. The re- search highlights EMMs as a valuable tool for advanced clustering tasks and provides insights into their potential applications in handling real-world datasets with complex covariance structures.