A variable step learning algorithm for Gaussian mixture models based on the Bhattacharyya coefficient and correlation coefficient criterion

Abstract

The expectation maximization (EM) algorithm is one of the most enduring ways to estimate the parameters of Gaussian mixture models. However, the EM algorithm needs to know in advance the true number of mixing components, and its performance highly depends on the initial parameters, which leads to use it difficultly in practice. To overcome the above two drawbacks, a variable step learning algorithm is proposed for learning a Gaussian mixture models. The novelty of the algorithm is that a variable step search strategy is proposed to find the actual number of Gaussian mixture components, or slightly above it. This number is obtained by maximizing the Bhattacharyya coefficient criterion, which in turn quantifies how close the Gaussian mixtures models fit the observed data. Furthermore, the initialization parameters are determined by the correlation coefficient criterion representing the shape characteristics between the new GMM and the histograms of the data. Based on these two criteria, the proposed algorithm can make both parameter learning and model selection more efficient, as shown by the conducted experiments.