Generalized bayesian factor analysis for integrative clustering with applications to multi-omics data

Integrative clustering is a clustering approach for multiple datasets, which provide different views of a common group of subjects. It enables analyzing multi-omics data jointly to, for example, identify the subtypes of diseases, cells, and so on, capturing the complex underlying biological processes more precisely. On the other hand, there has been a great deal of interest in incorporating the prior structural knowledge on the features into statistical analyses over the past decade. The knowledge on the gene regulatory network (pathways) can potentially be incorporated into many genomic studies. In this paper, we propose a novel integrative clustering method which can incorporate the prior graph knowledge. We first develop a generalized Bayesian factor analysis (GBFA) framework, a sparse Bayesian factor analysis which can take into account the graph information. Our GBFA framework employs the spike and slab lasso (SSL) prior to impose sparsity on the factor loadings and the Markov random field (MRF) prior to encourage smoothing over the adjacent factor loadings, which establishes a unified shrinkage adaptive to the loading size and the graph structure. Then, we use the framework to extend iCluster+, a factor analysis based integrative clustering approach. A novel variational EM algorithm is proposed to efficiently estimate the MAP estimator for the factor loadings. Extensive simulation studies and the application to the NCI60 cell line dataset demonstrate that the propose method is superior and delivers more biologically meaningful outcomes.