Fast Monte-Carlo algorithms for finding low-rank approximations

Journal of the ACM

Volumn 51, Issue 6, 2004, Pages 1025-1041

  Frieze, Alan ^a   Kannan, Ravi ^b,d   Vempala, Santosh ^c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b YALE UNIVERSITY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d Yale University   (United States)

Author keywords

Low rank approximation; Matrix algorithms; Sampling

Indexed keywords

FROBENIUS NORM; LOW-RANK APPROXIMATION; MATRIX ALGORITHMS; SINGULAR VALUE DECOMPOSITION (SVD);

APPROXIMATION THEORY; DATA STORAGE EQUIPMENT; INFORMATION RETRIEVAL; MATRIX ALGEBRA; MONTE CARLO METHODS; POLYNOMIALS; PROBABILITY DISTRIBUTIONS; SAMPLING;

ALGORITHMS;

EID: 20444476106     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/1039488.1039494     Document Type: Article

References (20)

1. ACHLIOPTAS, D., AND MCSHERRY, F. 2001. Fast computation of low rank approximations. In Proceedings of the 33rd Annual Symposium on Theory of Computing. ACM, New York, pp. 611-618.
2. ALON, N., DUKE, R. A., LEFMANN, H., RÖDL, V., AND YUSTER, R. 1994. The algorithmic aspects of the regularity lemma, J. Algorithms 16, 80-109.
3. BAR-YOSSEF, Z. 2003. Sampling lower bounds via information theory. In Proceedings of the 35th Annual Symposium on Theory of Computing. ACM, New York, pp. 335-344.
4. BERRY, M. W., DUMAIS, S. T., AND O'BRJEN, G. W. 1995. Using linear algebra for intelligent information retrieval. SIAM Rev. 37, 4, 573-595.
5. DEERWESTER, S., DUMAIS, S. T., LANDAUER, T. K., FURNAS, G. W., AND HARSHMAN, R. A. 1990. Indexing by latent semantic analysis. J. Soc. Inf. Sci. 41, 6, 391-407.
6. DRINEAS, P., AND KANNAN, R. 2001. Fast Monte-Carlo algorithms for approximate matrix multiplication. In Proceedings of the 42nd IEEE Annual Symposium on the Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 452-459.
7. DRINEAS, P., AND KANNAN, R. 2003. Pass efficient algorithms for approximating large matrices. In Proceedings of the Symposium on Discrete Algorithms. ACM, New York, pp. 223-232.
8. DRINEAS, P., FRIEZE, A., KANNAN, R., VEMPALA, S., AND VINAY, V. 2004a. Clustering large graphs via the singular value decomposition. Mach. Learn. 56, 9-33.
9. DRINEAS, P., MAHONEY, M. W., AND KANNAN, R. 2004b. Fast monte carlo algorithms for matrices II: Computing low-rank approximations to a matrix. Tech. Rep. Yale University, YALEU/DCS/TR-1270, 2004.
10. DUMAIS, S. T. 1991. Improving the retrieval of information from external sources. Behav. Res. Meth. Instrum. Comput. 23, 2, 229-236.
11. DUMAIS, S. T., FURNAS, G. W., LANDAUER, T. K., AND DEERWESTER, S. 1988. Using latent semantic analysis to improve information retrieval. In Proceedings of CHI'88: Conference on Human Factors in Computing. ACM, New York, 281-285.
12. FRIEZE, A. M., AND KANNAN, R. 1996. The regularity lemma and approximation schemes for dense problems. In Proceedings of the 37th Annual IEEE Symposium on Foundations of Computing. IEEE Computer Society Press, Los Alamitos, Calif., pp. 12-20.
13. FRIEZE, A. M., AND KANNAN, R. 1999a. Quick approximations to matrices and applications. Combinatorica 19, 175-220.
14. FRIEZE, A. M., AND KANNAN, R. 1999b. A simple algorithm for constructing Szemeredi's Regularity Partition. Elect. J. Combinat. 6, 1, R17.
15. FRIEZE, A., KANNAN, R., AND VEMPALA, S. 1998. Fast Monte-Carlo algorithms for finding low-rank approximations. In Proceedings of 39th Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 370-378.
16. GOLUB, G. H., AND VAN LOAN, C. F. 1989. Matrix Computations, Johns Hopkins University Press, London, England.
17. KLEINBERG, J. 1999. Authoritative sources in a hyperlinked environment. JACM 46, 5, 604-632.
18. KOMLÓS, J., AND SIMONOVITS, M. 1996. Szemerédi's Regularity Lemma and its applications in graph theory. Combinatorics, Paul Erdos is Eighty, Bolyai Society Mathematical Studies, D. Miklos et al. Eds. 2, 295-352.
19. PAPADIMITRIOU, C., RAGHAVAN, P., TAMAKI, H., AND VEMPALA, S. 2000. Latent Semantic Indexing: A Probabilistic Analysis. J. Comput. Syst. Sci. 61, 217-235.
20. SZEMEREDI, E. 1978. Regular partitions of graphs. Proceedings, Colloque Inter. CNRS, J.-C. Bermond, J.-C. Fournier, M. Las Vergnas and D. Sotteau, Eds. 399-401.