Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms

doi:10.1073/pnas.0530258100

Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms

Departments of ^*Genetics and ^‡Biochemistry, Stanford University, Stanford, CA 94305

Contributed by David Botstein

Abstract

We describe a comparative mathematical framework for two genome-scale expression data sets. This framework formulates expression as superposition of the effects of regulatory programs, biological processes, and experimental artifacts common to both data sets, as well as those that are exclusive to one data set or the other, by using generalized singular value decomposition. This framework enables comparative reconstruction and classification of the genes and arrays of both data sets. We illustrate this framework with a comparison of yeast and human cell-cycle expression data sets.

Footnotes

↵ † To whom correspondence should be addressed. E-mail: orly{at}genome.stanford.edu.
↵ § In this article m̂ denotes a matrix, |v〉 denotes a column vector, and 〈u| denotes a row vector such that m̂|v〉, 〈u|m̂, and 〈u|v〉 all denote inner products, and |v〉〈u| denotes an outer product.
Abbreviations:
1. SVD, singular value decomposition
2. GSVD, generalized SVD