Bayesian inference of clustering and multiple Gaussian graphical models selection

We consider a Bayesian framework for clustering the high-dimensional data and learning sparse multiple graphical models simultaneously. Different from most previous multiple graphs learning methods which assume that the cluster information is known in advance, we impose a multi-distribution prior for the cluster labels. Then a joint spike-and-slab graphical lasso prior is imposed for the precision matrices, which can induce a sparsity and homogeneity of the heterogeneous graphical models across all clusters adaptively. Additionally, by imposing a structural Markov random field (MRF) prior, the proposed method can also cluster the network-linked data without the independence assumption of the samples. Then a fast Expectation Maximization (EM) algorithm is utilized for the posterior inference. The proposed model can get a significant improvement both in clustering error and graphical selection precision. The simulations and real data analysis are shown to demonstrate the performance of our method.