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

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