Fast updating algorithms for latent semantic indexing

Eugene Vecharynski, Yousef Saad

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

This paper discusses a few algorithms for updating the approximate singular value decomposition (SVD) in the context of information retrieval by latent semantic indexing (LSI) methods. A unifying framework is considered which is based on Rayleigh-Ritz projection methods. First, a Rayleigh-Ritz approach for the SVD is discussed and it is then used to interpret the Zha and Simon algorithms [SIAM J. Sci. Comput., 21 (1999),pp. 782-791]. This viewpoint leads to a few alternatives whose goal is to reduce computational cost and storage requirement by projection techniques that utilize subspaces of much smaller dimension. Numerical experiments show that the proposed algorithms yield accuracies comparable to those obtained from standard ones at a much lower computational cost.

Original languageEnglish (US)
Pages (from-to)1105-1131
Number of pages27
JournalSIAM Journal on Matrix Analysis and Applications
Volume35
Issue number3
DOIs
StatePublished - Jan 1 2014

Keywords

  • Latent semantic indexing
  • Low-rank approximation
  • Min-max characterization
  • Rayleigh-Ritz procedure
  • Ritz singular values
  • Ritz singular vectors
  • Singular value decomposition
  • Text mining
  • Updating algorithm

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