Spectral biclustering of microarray cancer data: co-clustering genes and conditions

Global analyses of RNA expression levels are useful for classifying genes and overall phenotypes. Often these classification problems are linked, and one wants to simultaneously find "marker genes" that are differentially expressed in particular “conditions”. We have developed a method that simultaneously clusters genes and conditions, finding distinctive "checkerboard" patterns in matrices of gene expression data, if they exist. In a cancer context, these checkerboards correspond to genes that are markedly up or down regulated in patients with particular types of tumors. Our method, spectral biclustering, is based on the observation that checkerboard structures in matrices of expression data can be found in eigenvectors corresponding to characteristic expression patterns across genes or conditions. Furthermore, these eigenvectors can be readily identified by commonly used linear-algebra approaches, in particular the singular value decomposition (SVD), coupled with closely integrated normalization steps. We present a number of variants of the approach, depending on whether the normalization over genes and conditions is done independently or in a coupled fashion. We then apply spectral biclustering to a selection of publicly available cancer expression data sets, and examine the degree to which it is able to identify checkerboard structures. Furthermore, we compare the performance of our biclustering methods against a number of reasonable benchmarks (e.g. direct application of SVD or normalized cuts to raw data).