Singular value decomposition of large random matrices (for two-way classification of microarrays)

Authors:
Marianna Bolla;Katalin Friedl;András Krámli
Affiliations:
Institute of Mathematics, Budapest University of Technology and Economics, Hungary;Department of Computer Science, Budapest University of Technology and Economics, Hungary;Bolyai Institute, University of Szeged, Hungary
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to random noise is investigated. It is proved that such an mxn random matrix almost surely has a constant number of large singular values (of order mn), while the rest of the singular values are of order m+n as m,n-~. We prove almost sure properties for the corresponding isotropic subspaces and for noisy correspondence matrices. An algorithm, applicable to two-way classification of microarrays, is also given that finds the underlying block structure.