Use of EM Algorithm for Classification Issues and Parameter Estimation in Gaussian Mixture Models

Abstract

One effective iterative method for estimating parameters in latent variable probabilistic models is the Expectation-Maximization (EM) algorithm, which finds extensive use in classification issues. A versatile probabilistic framework for modeling data from multiple Gaussian distributions, Gaussian Mixture Models (GMMs) employ EM for parameter estimation, which is explored in this article. Problems with class membership estimation (including means, covariances, and mixing coefficients) are the primary focus of this study. Starting with initial parameter estimations, estimating posterior probabilities in the E-step, and repeatedly updating model parameters in the M-step until convergence, the technique entails applying the EM algorithm on both synthetic and real-world datasets. In order to measure performance, we compare it to K-means and other baseline classifiers using measures like classification accuracy, Adjusted Rand Index (ARI), and log-likelihood progression. When data is distributed according to a multimodal Gaussian distribution, the findings show that EM-GMM provides better parameter estimation and better classification accuracy. Initialization procedures have a substantial effect on performance, as convergence study further shows. In addition to reiterating the EM algorithm's usefulness for probabilistic classification, this paper also describes its advantages and disadvantages and offers suggestions for improving its performance in settings with high-dimensional data and noise.