Matrices with Low-Rank-Plus-Shift Structure: Partial SVD and Latent Semantic Indexing

  • Authors:
  • Hongyuan Zha;Zhenyue Zhang

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 1999

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Abstract

We present a detailed analysis of matrices satisfying the so-called low-rank-plus-shift property in connection with the computation of their partial singular value decomposition (SVD). The application we have in mind is latent semantic indexing for information retrieval, where the term-document matrices generated from a text corpus approximately satisfy this property. The analysis is motivated by developing more efficient methods for computing and updating partial SVD of large term-document matrices and gaining deeper understanding of the behavior of the methods in the presence of noise.