Matrices, vector spaces, and information retrieval

SIAM Review

Volumn 41, Issue 2, 1999, Pages 335-362

  Berry, Michael W ^a   Drmač, Zlatko ^b   Jessup, Elizabeth R ^b  

^a University of Tennessee   (United States)

^b University of Colorado   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA STRUCTURES; DATABASE SYSTEMS; DIGITAL COMPUTERS; INFORMATION RETRIEVAL; MATHEMATICAL TRANSFORMATIONS; VECTORS;

DIGITAL LIBRARIES; ORTHOGONAL FACTORIZATION; SINGULAR VALUE DECOMPOSITION; VECTOR SPACES;

LINEAR ALGEBRA;

EID: 0032624581     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144598347035     Document Type: Article

References (60)

1. E. ANDERSON, Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, S. OSTROUCHOV, AND D. SORENSEN, LAPACK Users' Guide, 2nd ed., SIAM, Philadelphia, PA, 1995.
2. H. ANDREWS AND C. PATTERSON, Outer product expansions and their uses in digital image processing, Amer. Math. Monthly, 82 (1975), pp. 1-13.
3. R. BARRETT, M. BERRY, T. F. CHAN, J. DEMMEL, J. DONATO, J. DONGARRA, V. EIJKHOUT, R. POZO, C. ROMINE, AND H. VAN DER VORST, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA, 1994.
4. D. BERG, A Guide to the Oxford English Dictionary, Oxford University Press, Oxford, UK, 1993.
5. M. BERRY, Large scale singular value computations, Internat. J. Supercomputer Applications, 6 (1992), pp. 13-49.
6. M. BERRY, SVDPACK: A Fortran 77 Software Library for the Sparse Singular Value Decomposition, Tech. Rep. CS-92-159, University of Tennessee, Knoxville, TN, June 1992.
7. M. BERRY, Survey of public-domain Lanczos-based software, in Proceedings of the Cornelius Lanczos Centenary Conference, J. Brown, M. Chu, D. Ellison, and R. Plemmons, eds., 1997, SIAM, Philadelphia, PA, pp. 332-334.
8. M. BERRY, T. DO, G. O'BRIEN, V. KRISHNA, AND S. VARADHAN, SVDPACKC: Version 1.0 User's Guide, Tech. Rep. CS-93-194, University of Tennessee, Knoxville, TN, October 1993.
9. M. W. BERRY, S. T. DUMAIS, AND G. W. O'BRIEN, Using linear algebra for intelligent information retrieval, SIAM Rev., 37 (1995), pp. 573-595.
10. M. BERRY AND R. FIERRO, Low-rank orthogonal decompositions for information retrieval applications, Numer. Linear Algebra Appl., 3 (1996), pp. 301-328.
11. M. BERRY, B. HENDRICKSON, AND P. RAGHAVAN, Sparse matrix reordering schemes for browsing hypertext, in Lectures in Appl. Math. 32: The Mathematics of Numerical Analysis, J. Renegar, M. Shub, and S. Smale, eds., AMS, Providence, RI, 1996, pp. 99-123.
12. M. BERRY AND D. WITTER, Intelligent information management using latent semantic indexing, in Proceedings of Interface'97, Interface of North America Foundation, Fairfax Station, VA, 1997.
13. K. BHARAT AND A. BRODER, Estimating the relative size and overlap of public web search engines, in 7th International World Wide Web Conference, paper FP37, Elsevier Science, New York, 1998.
14. A. BJÖRCK, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA, 1996.
15. D. BOGARD, ED., The Bowker Annual Library and Book Trade Almanac, 43rd ed., R.R. Bowker, New Providence, NJ, 1998.
16. Books in Print, R.R. Bowker, New York, 1997/1998.
17. R. BORDING, A. GERTSZTENKORN, L. LINES, J. SCALES, AND S. TREITEL, Applications of seismic travel-time tomography, Geophys. J. R. Astr. Soc., 90 (1987), pp. 285-304.
18. C. BUCKLEY, G. SALTON, J. ALLAN, AND A. SINGHANL, Automatic query expansion using SMART: TREC 3, in Overview of the Third Text REtrieval Conference, D. Harman, ed., National Institute of Standards and Technology Special Publication 500-226, NIST, Gaithersburg, MD, April 1995, pp. 69-80.
19. S. DEERWESTER, S. DUMAIS, G. FURNAS, T. LANDAUER, AND R. HARSHMAN, Indexing by latent semantic analysis, J. American Society for Information Science, 41 (1990), pp. 391-407.
20. S. DUMAIS, Improving the retrieval of information from external sources, Behavior Research Methods, Instruments, & Computers, 23 (1991), pp. 229-236.
21. S. DUMAIS, LSI meets TREC: A status report, in The First Text REtrieval Conference, D. Harman, ed., National Institute of Standards and Technology Special Publication 500-207, NIST, Gaithersburg, MD, March 1993, pp. 137-152.
22. S. DUMAIS, Latent Semantic Indexing (LSI) and TREC-2, in The Second Text REtrieval Conference, D. Harman, ed., National Institute of Standards and Technology Special Publication 500-215, NIST, Gaithersburg, MD, March 1994, pp. 105-116.
23. C. ECKART AND G. YOUNG, The approximation of one matrix by another of lower rank, Psychometrika, 1 (1936), pp. 211-218.
24. P. FOLTZ AND S. DUMAIS, Personalized information delivery: An analysis of information filtering methods, Comm. ACM, 35 (1992), pp. 51-60.
25. W. FRAKES AND R. BAEZA-YATES, Information Retrieval: Data Structures & Algorithms, Prentice-Hall, Englewood Cliffs, NJ, 1992.
26. G. GOLUB AND C. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
27. G. H. GOLUB, V. KLEMA, AND G. W. STEWART, Rank Degeneracy and Least Squares Problems, Tech. Rep. TR-456, Department of Computer Science, University of Maryland, College Park, 1976.
28. D. HARMAN, Overview of the third text REtrieval conference (TREC-3), in Overview of the Third Text REtrieval Conference, D. Harman, ed., National Institute of Standards and Technology Special Publication 500-226, NIST, Gaithersburg, MD, April 1995, pp. 1-21.
29. D. HARMAN AND E. VOORHEES, Overview of the fifth text REtrieval conference (TREC-5), in Information Technology: The Fifth Text REtrieval Conference (TREC-5), D. Harman and E. Voorhees, eds., National Institute of Standards and Technology Special Publication 500-238, NIST, Gaithersburg, MD, November 1996, pp. 1-28.
30. W. JONES AND G. FURNAS, Pictures of relevance: A geometric analysis of similarity measures, J. American Society for Information Science, 38 (1987), pp. 420-442.
31. W. KAHAN, Conserving Confluence Curbs Ill-Conditioning, Tech. Rep. 6, Computer Science Department, University of California, Berkeley, 1972.
32. T. KOLDA AND D. O'LEARY, A semi-discrete matrix decomposition for latent semantic indexing in information retrieval, ACM Trans. Inform. Systems, 16 (1998), pp. 322-346.
33. G. KOWALSKI, Information Retrieval Systems: Theory and Implementation, Kluwer Academic Publishers, Boston, 1997.
34. C. LANCZOS, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45 (1950), pp. 255-282.
35. S. LAWRENCE AND C. GILES, Searching the world wide web, Science, 280 (1998), pp. 98-100.
36. R. LEHOUCQ, Analysis and Implementation of an Implicitly Restarted Arnoldi Iteration, Ph.D. Thesis, Rice University, Houston, TX, 1995.
37. R. LEHOUCQ AND D. SORENSEN, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 789-821.
38. T. LETSCHE AND M. BERRY, Large-scale information retrieval with latent semantic indexing, Inform. Sci., 100 (1997), pp. 105-137.
39. Library of Congress, http://lcweb.loc.gov/, April 24, 1998.
40. J. LOVINS, Development of a stemming algorithm, Mechanical Translation and Computational Linguistics, 11 (1968), pp. 22-31.
41. MEDLINE, ftp://ftp.cs.cornell.edu/pub/smart/med/, May 27, 1998.
42. L. MIRSKY, Symmetric gauge functions and unitarily invariant norms, Quart. J. Math., 11 (1960), pp. 50-59.
43. C. MOLER AND D. MORRISON, Singular value analysis of cryptograms, Amer. Math. Monthly, 90 (1983), pp. 78-87.
44. G. O'BRIEN, Information Management Tools for Updating an SVD-Encoded Indexing Scheme, Master's Thesis, University of Tennessee, Knoxville, TN, 1994.
45. B. PARLETT, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.
46. L. RABINER AND R. SCHAFER, Digital Processing of Speech Signals, 1st ed., Prentice-Hall, Englewood Cliffs, NJ, 1978.
47. H. RUTISHAUSER, Simultaneous iteration method for symmetric matrices, Numer. Math., 16 (1970), pp. 205-223.
48. G. SALTON, Automatic Information Organization and Retrieval, McGraw-Hill, New York, 1968.
49. G. SALTON AND C. BUCKLEY, Improving retrieval performance by relevance feedback, J. American Society for Information Science, 41 (1990), pp. 288-297.
50. G. SALTON AND M. MCGILL, Introduction to Modern Information Retrieval, McGraw-Hill, New York, 1983.
51. A. H. SAMEH AND J. A. WISNIEWSKI, A trace minimization algorithm for the generalized eigenvalue problem, SIAM J. Numer. Anal., 19 (1982), pp. 1243-1259.
52. J. SCALES, P. DOCHERY, AND A. GERSZTERNKORN, Regularization of nonlinear inverse problems: Imaging the near-surface weathering layer, Inverse Problems, 6 (1990), pp. 115-131.
53. Search Engine Watch, http://www.searchenginewatch.com/, March 25, 1998.
54. H. SIMON AND H. ZHA, On Updating Problems in Latent Semantic Indexing, Tech. Rep. CSE-97-011, The Pennsylvania State University, University Park, PA, 1997.
55. K. SPARCK JONES, A statistical interpretation of term specificity and its applications in retrieval, J. Documentation, 28 (1972), pp. 11-21.
56. G. W. STEWART, Rank degeneracy, SIAM J. Sci. Statist. Comput., 5 (1984), pp. 403-413.
57. TIPSTER, http://www.tipster.org, May 28, 1998.
58. Ulrich's International Periodicals Directory, R.R. Bowker, New York, 1998.
59. S. VARADHAN, M. BERRY, AND G. GOLUB, Approximating dominant singular triplets of large sparse matrices via modified moments, Numer. Algorithms, 13 (1996), pp. 123-152.
60. D. WITTER, Downdating the Latent Semantic Indexing Model for Information Retrieval, Master's Thesis, University of Tennessee, Knoxville, TN, 1997.