  Bi-clustering is a useful approach in analyzing biological data when
observations come from heterogeneous groups and have a large number of
features. We outline a general Bayesian approach in tackling bi-clustering
problems in moderate to high dimensions, and propose three Bayesian
bi-clustering models on categorical data, which increase in complexities in
their modeling of the distributions of features across bi-clusters. Our
proposed methods apply to a wide range of scenarios: from situations where data
are cluster-distinguishable only among a small subset of features but masked by
a large amount of noise, to situations where different groups of data are
identified by different sets of features or data exhibit hierarchical
structures. Through simulation studies, we show that our methods outperform
existing (bi-)clustering methods in both identifying clusters and recovering
feature distributional patterns across bi-clusters. We apply our methods to two
genetic datasets, though the area of application of our methods is even
broader.
