A logistic function for Expectation-Maximization Algorithm with split and merge

Abstract

The Expectation-Maximization (EM) algorithm provides a framework for finding maximum likelihood estimates of parameters in statistical models. But the algorithm has challenges which include converging to local optima, initialization sensitivity, convergence speed, etc. To seek solutions to these challenges, this paper reviews 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 aim of this paper is to implement a logistic function in the split and merge components of the EM algorithm. This extension was then applied to both simulated and real data. The simulated data is generated from the Gaussian mixture while real data is on 553 diabetic patients. The extended algorithm selected a 4component Gaussian mixture with good estimates of the parameter. It also selected a 4-component Gaussian mixture for real data set with 95.1% rate of convergence with 80 iterations. This shows that, the application of the extended algorithm to both datasets indicate an improvement in the algorithm.