Analysis of the singular value decomposition as a tool for processing microarray expression data

We give two informative derivations of a spectral algorithm for clustering and partitioning a bi-partite graph. In the first case we begin with a discrete optimization problem that relaxes into a tractable continuous analogue. In the second case we use the power method to derive an iterative interpretation of the algorithm. Both versions reveal a natural approach for re-scaling the edge weights and help to explain the performance of the algorithm in the presence of outliers. Our motivation for this work is in the analysis of microarray data from bioinformatics, and we give some numerical results for a publicly available acute leukemia data set.