Two-way clustering, or biclustering, of gene expression data searches for local patterns of gene expression. A bicluster (or a two-way cluster) is defined as a set of genes whose expression profiles are mutually similar within a subset of experimental conditions/samples. Two-way clustering has more flexibility and can model gene transcription more precisely than traditional clustering. I proposed a Bayesian biclustering model (BBC) and implemented a Gibbs sampling procedure for its statistical inference. I showed that the Bayesian biclustering model can correctly identify multiple clusters of gene expression data. I conducted a comprehensive comparison of biclustering results by four operation characteristics. Using simulated data both from the model and with realistic characters, I demonstrated the BBC algorithm outperforms other methods in both robustness and accuracy. I also showed that the model is stable for two normalization methods, the interquartile range normalization and the smallest quartile range normalization.

Applying the BBC algorithm to the yeast expression data, I observed that majority of the biclusters found by BBC are supported by significant biological evidences, such as enrichments of gene functions and transcription factor binding sites in the corresponding promoter sequences. Bayesian two-way clustering, as a rigorous model, has the ability to analyze multiple types of data integratively. I developed a Bayesian biclustering model for discrete data and a general Bayesian two-way clustering framework for hybrid type of genomic data. I also discussed another Bayesian two-way clustering model for binary data inspired by probit regression model. In addition I explored the connection of two-way clustering and matrix factorization, and showed that the Bayesian two-way clustering model can be viewed as a special type of sparse matrix factorization.