A Novel Split and Merge EM Algorithm for Gaussian Mixture Model

As an extremely powerful probability model, Gaussian mixture model (GMM) has been widely used in fields of pattern recognition, information processing and data mining. If the number of the Gaussians in the mixture is pre-known, the well-known Expectation-Maximization (EM) algorithm could be used to estimate the parameters in the Gaussian mixture model. However, in many practical applications, the number of the components is not known.Then the Gaussian mixture modeling becomes a compound problem of the determination of number of Gaussian components and the parameter estimation for the mixture, which is rather difficult. In this paper, we propose a split and merge EM (SMEM) algorithm to decide the number of the components, which is referred to the model selection for the mixture. Based on the minimum description length (MDL) criterion, the proposed SMEM algorithm can avoid the local optimum drawback of the usual EM algorithm and determine the number of components in the Gaussian mixture model automatically. By splitting and merging the uncorrect components, the algorithm can converge to the maximization of the MDL criterion function and get a better parameter estimation of the Gaussian mixture with correct number of components in the mixture. It is demonstrated well by the experiments that the proposed split and merge EM algorithm can make both parameter learning and model selection efficiently for Gaussian mixture.