Competitve stop mahalanobis distance based EM algorithm for Gaussian mixture model

This paper proposes a competitive stop Mahalanobis distance based expectation-maximization (CSMDEM) algorithm for learning a Gaussian mixture model (GMM) from multivariate data. This algorithm embeds a splitting failure condition and a competitive stop condition into the original Mahalanobis distance based EM (MDEM) algorithm. The goal of introducing the above two conditions is to avoid over-splitting suffered in MDEM algorithm. The splitting failure condition is based on Lilliefors test which is performed to determine the necessary of applying a discriminant to split and accelerate the satisfy of competitive stop condition. This stop condition is based on minimum description length variant (MDL₂) criterion. It competes with the usual stop condition-no cluster deviates from the multivariate Gaussian distribution. Experimental results are presented against MDEM algorithm on artificially generated data-sets. The experimental results demonstrate that the proposed CSMDEM algorithm has an increased capability to find the parameters of GMM, while maintaining a low average number of EM iterations.