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

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  • Bolla, Marianna
  • Friedl, Katalin
  • Krámli, András

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 ), while the rest of the singular values are of order as m,n-->[infinity]. 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.

Suggested Citation

  • Bolla, Marianna & Friedl, Katalin & Krámli, András, 2010. "Singular value decomposition of large random matrices (for two-way classification of microarrays)," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 434-446, February.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:434-446
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    References listed on IDEAS

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    1. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
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