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Efficient Computation of the Riemannian SVD in Total Least Squares Problems in Information Retrieval

In: Total Least Squares and Errors-in-Variables Modeling

Author

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  • Ricardo D. Fierro

    (California State University, Department of Mathematics)

  • Michael W. Berry

    (University of Tennessee, Department of Computer Science)

Abstract

Recently, a nonlinear generalization of the singular value decomposition (SVD), called the Riemannian-SVD (R-SVD), for solving full rank total least squares problems was extended to low rank matrices within the context of latent semantic indexing (LSI) in information retrieval. This new approach, called RSVD-LSI, is based on the full SVD of an m × n term-by-document matrix A and requires the dense m × m left singular matrix U and the n × n right singular matrix V. Here, m corresponds to the size of the dictionary and n corresponds to the number of documents. We dicuss this method along with an efficient implementation of the method that takes into account the sparsity of A.

Suggested Citation

  • Ricardo D. Fierro & Michael W. Berry, 2002. "Efficient Computation of the Riemannian SVD in Total Least Squares Problems in Information Retrieval," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 353-364, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_31
    DOI: 10.1007/978-94-017-3552-0_31
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