基于最大后验估计的无监督聚类算法

Unsupervised clustering algorithm based on Maximum a Posteriori

传统的基于EM算法的聚类方法,当模型的某个高斯分量的协方差矩阵变为奇异矩阵时,会导致聚类失败。提出在聚类过程中用最大后验估计(MAP)来代替极大似然估计(MLE);将一种改进的贝叶斯信息准则(BIC)与模型参数估计同时处理,扩大了模型选择的搜索范围。该算法有效地避免了协方差矩阵在迭代中陷入奇异,并将参数估计和模型选择同时进行。通过R软件进行仿真分析,结过表明改进的算法在减少计算量同时,提高了聚类的准确度,并具有鲁棒性。

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.