Abstract
The Riemannian SVD (or R-SVD) is a recent nonlinear generalization of the SVD which has been used for specific applications in systems and control. This decomposition can be modified and used to formulate a filtering-based implementation of Latent Semantic Indexing (LSI) for conceptual information retrieval. With LSI, the underlying semantic structure of a collection is represented in k-dimensional space using a rank-k approximation to the corresponding (sparse) term-bydocument matrix. Updating LSI models based on user feedback can be accomplished using constraints modeled by the R-SVD of a low-rank approximation to the original term-by-document matrix.
Preview
Unable to display preview. Download preview PDF.
References
M. Berry, S. Dumais and G. O'Brien (1995). Using Linear Algebra for Intelligent Information Retrieval, SIAM Review, 37:4:573–595.
S. Deerwester, S. Dumais, G. Furnas, T. Landauer and R. Harshman (1990). Indexing by Latent Semantic Analysis, Journal of the American Society for Information Science, 41(6):391–409.
S. T. Dumais (1991). Improving the Retrieval from External Sources, Behavior Research Methods, Instruments, & Computers, 23(2):229–236.
B. De Moor (1993). Structured Total Least Squares and L 2 Approximation Problems, Linear Algebra and its Applications, 188,189:163–205.
G. Golub and C. Van Loan (1996). Matrix Computations, John-Hopkins, Baltimore, Third Ed.
S. Van Huffel and J. Vandewalle (1991). The Total Least Squares Problems: Computational Aspects and Analysis, SIAM, Philadelphia; PA.
E. P. Jiang (1998). Information Retrieval and Filtering Using the Riemannian SVD, Ph.D. Thesis, Dept. of Computer Science, The University of Tennessee, Knoxville, TN.
T. A. Letsche and M. Berry (1997). Large Scale Information Retrieval with Latent Semantic Indexing, Information Sciences, 100:105–137.
L. Mirsky (1960). Symmetric Gage Function and Unitarily Invariant Norms, Q. J. Math, 11:50–59.
G. Salton and C. Buckley (1990). Improving Retrieval Performance by Relevance Feedback, J. Amer. Soc. Info. Sci., 41:288–197.
H. Zha (1991). The Restricted Singular Value Decomposition of Matrix Triplets, SIAM J. Matrix Anal. Appl., 12(1):172–194.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiang, E.P., Berry, M.W. (1998). Information filtering using the Riemannian SVD (R-SVD). In: Ferreira, A., Rolim, J., Simon, H., Teng, SH. (eds) Solving Irregularly Structured Problems in Parallel. IRREGULAR 1998. Lecture Notes in Computer Science, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018555
Download citation
DOI: https://doi.org/10.1007/BFb0018555
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64809-3
Online ISBN: 978-3-540-68533-3
eBook Packages: Springer Book Archive