Information filtering using the Riemannian SVD (R-SVD)

Jiang, Eric; Berry, Michael W.

doi:10.1007/bfb0018555

Cited by 11 publications

(7 citation statements)

References 9 publications

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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: 91%

“…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%

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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: 91%

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%

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Lanczos and the Riemannian SVD in information retrieval applications

Fierro

Jiang

2005

Numer. Linear Algebra Appl.

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“…The semidiscrete decomposition (SDD) has been proposed to reduce the storage and computational costs of LSI [15]. It has been shown that user feedback can be integrated into LSI models by using the Riemannian SVD (R-SVD) [13]. Compared with these studies, the algorithm presented here differs in that it focuses on improving the precision of simi-INote that this is essentially different from scaling or normalizing of vectors as a preprocass or a post-process of SVD mentioned in [5].…”

Section: Introductionmentioning

confidence: 99%

Latent semantic space

Ando

2000

Proceedings of the 23rd Annual International ACM SIGIR Conference on Research and Development in Information Retrieval

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We present a novel algorithm that creates document vectors with reduced dimensionality. This work was motivated by an application characterizing relationships among documents in a collection. Our algorithm yielded inter-document similarities with an average precision up to 17.8% higher than that of singular value decomposition (SVD) used for Latent Semantic Indexing. The best performance was achieved with dimensional reduction rates that were 43% higher than SVD on average. Our algorithm creates basis vectors for a reduced space by iteratively "scaling" vectors and computing eigenvectors. Unlike SVD, it breaks the symmetry of documents and terms to capture information more evenly across documents. We also discuss correlation with a probabilistic model and evaluate a method for selecting the dimensionality using log-likelihood estimation.

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“…It has applications in such areas as least squares problems [26,28,51], in computing the pseudoinverse [26], in computing the Jordan canonical form [29]. In addition, SVD is used in solving integral equations [39], in digital image processing [4], in information retrieval [45], in seismic reflection tomography [10,23], and in optimization [5].…”

mentioning

confidence: 99%

An improved parallel singular value algorithm and its implementation for multicore hardware

Haidar

Kurzak

Łuszczek

2013

Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis

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The enormous gap between the high-performance capabilities of today's CPUs and off-chip communication poses extreme challenges to the development of numerical software that is scalable and achieves high performance.In this article, we describe a successful methodology to address these challenges-starting with our algorithm design, through kernel optimization and tuning, and finishing with our programming model. All these lead to development of a scalable high-performance Singular Value Decomposition (SVD) solver. We developed a set of highly optimized kernels and combined them with advanced optimization techniques that feature fine-grain and cache-contained kernels, a task based approach, and hybrid execution and scheduling runtime, all of which significantly increase the performance of our SVD solver.Our results demonstrate a many-fold performance increase compared to currently available software. In particular, our software is two times faster than Intel's Math Kernel Library (MKL), a highly optimized implementation from the hardware vendor, when all the singular vectors are requested; it achieves a 5-fold speed-up when only 20% of the vectors are computed; and it is up to 10 times faster if only the singular values are required.

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Information filtering using the Riemannian SVD (R-SVD)

Cited by 11 publications

References 9 publications

Lanczos and the Riemannian SVD in information retrieval applications

Lanczos and the Riemannian SVD in information retrieval applications

Latent semantic space

An improved parallel singular value algorithm and its implementation for multicore hardware

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