关键词: 混合模型, EM算法, 最大后验估计（MAP）, 模型选择, 聚类

Abstract: When EM method is used to estimate the maximum likelihood of models, the method will fail because of the covariance matrix become singularity matrix. This paper replaces the Maximum Likelihood Estimation（MLE） by a Maximum a Posteriori（MAP） estimator. By using the improved BIC criterion and the model parameter estimation at the same time, it can enlarge the area of model selection. The algorithm is effective to avoid singularity in the iterations, and uses the improved BIC criterion and the model parameter estimation at the same time. Finally, the R simulation results show that the proposed algorithm decreases the calculation, and improves the accuracy of the cluster, it also has strong robustness.

Key words: mixture model, EM algorithm, Maximum a Posteriori（MAP）, model selection, clustering