Abstract

This chapter describes a clustering procedure for microarray expression data based on a well-defined statistical model, specifically, a conjugate Dirichlet process mixture model. The clustering algorithm groups genes whose latent variables governing expression are equal, that is, genes belonging to the same mixture component. The model is fit with Markov chain Monte Carlo and the computational burden is eased by exploiting conjugacy. This chapter introduces a method to get a point estimate of the true clustering based on least-squares distances from the posterior probability that two genes are clustered. Unlike ad hoc clustering methods, the model provides measures of uncertainty about the clustering. Further, the model automatically estimates the number of clusters and quantifies uncertainty about this important parameter. The method is compared to other clustering methods in a simulation study. Finally, the method is demonstrated with actual microarray data.

Introduction

The main goal of clustering microarray data is to group genes that present highly correlated data; this correlation may reflect underlying biological factors of interest, such as regulation by a common transcription factor. A variety of heuristic clustering methods exist, including k-means clustering (MacQueen 1967) and hierarchical agglomerative clustering. These methods have had an enormous impact in genomics (Eisen et al. 1998) and are intuitively appealing. Nevertheless, the statistical properties of these heuristic clustering methods are generally not known. Model-based clustering procedures have been proposed for microarray data, including (1) the MCLUST procedure of Fraley and Raftery (2002) and Yeung et al. (2001), and (2) the Bayesian mixture model based clustering of Medvedovic and Sivaganesan (2002) and Medvedovic et al. (2004).