Biological and statistical evaluation of clusterings of gene expression profiles

Recent research on large-scale analysis of gene expression data explored the use of clustering algorithms to find groups of genes with similar expression profiles. An open problem is that it is not clear how the clusterings from different algorithms should be compared. We therefore discuss potential methods for evaluation of clusterings, including both context-independent statistical methods and methods based on systematic comparison of clusterings with gene annotation. Through a comparison study on example expression data, we find that context-independent evaluation methods may give misleading results, since they do not correspond well with annotation-based methods. We compare the context-independent methods (compactness and isolation) with a correlation-based evaluation method. We also propose a method based on computing the relative entropy of each cluster, under the hypothesis that biologically significant clusters should deviate significantly from the background distribution of the data set. This method may be used with any annotation that gives a classification of the genes, and it can be used when only some of the genes are annotated. We evaluate the method using enzyme classification as annotation in a data set where half of the genes are annotated with enzyme classes.