  Clustering is one of the most widely used procedures in the analysis of
microarray data, for example with the goal of discovering cancer subtypes based
on observed heterogeneity of genetic marks between different tissues. It is
well-known that in such high-dimensional settings, the existence of many noise
variables can overwhelm the few signals embedded in the high-dimensional space.
We propose a novel Bayesian approach based on Dirichlet process with a sparsity
prior that simultaneous performs variable selection and clustering, and also
discover variables that only distinguish a subset of the cluster components.
Unlike previous Bayesian formulations, we use Dirichlet process (DP) for both
clustering of samples as well as for regularizing the high-dimensional
mean/variance structure. To solve the computational challenge brought by this
double usage of DP, we propose to make use of a sequential sampling scheme
embedded within Markov chain Monte Carlo (MCMC) updates to improve the naive
implementation of existing algorithms for DP mixture models. Our method is
demonstrated on a simulation study and illustrated with the leukemia gene
expression dataset.
