Scoring clustering solutions by their biological relevance

Motivation: A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering gene expression data into homogeneous groups was shown to be instrumental in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on clustering algorithms for gene expression analysis, very few works addressed the systematic comparison and evaluation of clustering results. Typically, different clustering algorithms yield different clustering solutions on the same data, and there is no agreed upon guideline for choosing among them. Results: We developed a novel statistically based method for assessing a clustering solution according to prior biological knowledge. Our method can be used to compare different clustering solutions or to optimize the parameters of a clustering algorithm. The method is based on projecting vectors of biological attributes of the clustered elements onto the real line, such that the ratio of between-groups and within-group variance estimators is maximized. The projected data are then scored using a non-parametric analysis of variance test, and the score's confidence is evaluated. We validate our approach using simulated data and show that our scoring method outperforms several extant methods, including the separation to homogeneity ratio and the silhouette measure. We apply our method to evaluate results of several clustering methods on yeast cell-cycle gene expression data.