Solving total least-squares problems in information retrieval

Jiang, Eric; Berry, Michael W.

doi:10.1016/s0024-3795(00)00030-6

Cited by 18 publications

(14 citation statements)

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“…Details of the inverse iteration algorithm RINVIT for computing B can be found in Reference [15]. This new model B generally has nearly the same rank as A k , and numerical results in References [14,15] demonstrate that its rank-k matrix approximation…”

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 98%

“…The R-SVD can further be generalized to low-rank matrices and therefore used to formulate an enhanced LSI implementation (RSVD-LSI) for information retrieval [14,15]. The main idea here is to replace the matrix A k obtained from the SVD of A with a new matrix B subject to certain constraints, with the hope the semantic model derived from B gives improved document retrieval compared to A k .…”

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 99%

“…Suppose A k (Equation (2)) has the splitting where A F k denotes a portion of A k whose term-document associations are not allowed to change, and A C k the complement of A F k . The actual splitting scheme is determined by an m × n matrix P, which is typically determined by user feedback [14,15]. P speciÿes the set of terms and the set of documents of A k whose term-document associations are unperturbed according to A …”

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 99%

“…As shown in Reference [15], the solution of (Equation (6)) can be expressed in terms of the generalized singular triplet (u; ; v) corresponding to the minimal that satisÿes (Equation (7)):…”

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 99%

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Lanczos and the Riemannian SVD in information retrieval applications

Fierro

Jiang

2005

Numer. Linear Algebra Appl.

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SUMMARYVariations of the latent semantic indexing (LSI) method in information retrieval (IR) require the computation of singular subspaces associated with the k dominant singular values of a large m × n sparse matrix A, where k min(m; n). The Riemannian SVD was recently generalized to low-rank matrices arising in IR and shown to be an e ective approach for formulating an enhanced semantic model that captures the latent term-document structure of the data. However, in terms of storage and computation requirements, its implementation can be much improved for large-scale applications. We discuss an ecient and reliable algorithm, called SPK-RSVD-LSI, as an alternative approach for deriving the enhanced semantic model. The algorithm combines the generalized Riemannian SVD and the Lanczos method with full reorthogonalization and explicit restart strategies. We demonstrate that our approach performs as well as the original low-rank Riemannian SVD method by comparing their retrieval performance on a well-known benchmark document collection.

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Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 98%

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 99%

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 99%

Section: The Riemannian Svd (R-svd) and The Rsvd-lsi Modelmentioning

confidence: 99%

See 2 more Smart Citations

Lanczos and the Riemannian SVD in information retrieval applications

Fierro

Jiang

2005

Numer. Linear Algebra Appl.

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show abstract

“…7. [BR99], [Ber01], [BB05], [BF96], [BDJ99], [BO98], [Blo99], [BR01], [Dum91], [HB00], [JL00], [JB00], [LB97], [WB98], [ZBR01], [ZMS98] LSI and the truncated singular value decomposition dominated text mining research in the 1990s. 8.…”

Section: [Mey00] If the Term-by-document Matrix A M×n Has The Singulamentioning

confidence: 99%