Analysis of a Gibbs sampler method for model based clustering of gene   expression data
  Over the last decade, a large variety of clustering algorithms have been developed to detect coregulatory relationships among genes from microarray gene expression data. Model based clustering approaches have emerged as statistically well grounded methods, but the properties of these algorithms when applied to large-scale data sets are not always well understood. An in-depth analysis can reveal important insights about the performance of the algorithm, the expected quality of the output clusters, and the possibilities for extracting more relevant information out of a particular data set. We have extended an existing algorithm for model based clustering of genes to simultaneously cluster genes and conditions, and used three large compendia of gene expression data for S. cerevisiae to analyze its properties. The algorithm uses a Bayesian approach and a Gibbs sampling procedure to iteratively update the cluster assignment of each gene and condition. For large-scale data sets, the posterior distribution is strongly peaked on a limited number of equiprobable clusterings. A GO annotation analysis shows that these local maxima are all biologically equally significant, and that simultaneously clustering genes and conditions performs better than only clustering genes and assuming independent conditions. A collection of distinct equivalent clusterings can be summarized as a weighted graph on the set of genes, from which we extract fuzzy, overlapping clusters using a graph spectral method. The cores of these fuzzy clusters contain tight sets of strongly coexpressed genes, while the overlaps exhibit relations between genes showing only partial coexpression. 
Anagha Joshi, Yves Van de Peer, Tom Michoel