Column subset selection via sparse approximation of SVD

Theoretical Computer Science

Volumn 421, Issue , 2012, Pages 1-14

  Civril A ^a   Magdon Ismail, M ^b  

^a MELIKSAH UNIVERSITY   (Turkey)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Sparse approximation; Subset selection; SVD

Indexed keywords

CONSTRUCTED MATRICES; DETERMINISTIC APPROACH; EMPIRICAL RESULTS; EXISTENCE RESULTS; FROBENIUS NORM; GREEDY ALGORITHMS; MATRIX; OUTER PRODUCT; QR FACTORIZATIONS; RANDOMIZED ALGORITHMS; REAL MATRICES; SINGULAR VALUES; SINGULAR VECTORS; SPARSE APPROXIMATIONS; SUBSET SELECTION;

MATRIX ALGEBRA; SINGULAR VALUE DECOMPOSITION;

APPROXIMATION ALGORITHMS;

EID: 84856610315     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2011.11.019     Document Type: Article

References (35)

1. D. Achlioptas, F. McSherry, Fast computation of low rank matrix approximations, in: STOC'01: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, 2001, pp. 611618. (Pubitemid 32865778)
2. M. Berry, T. Do, G. O'Brien, V. Krishna, S. Varadhan, SVDPACKC (version 1.0) user's guide. Technical Report, University of Tennessee, 1993.
3. C. Boutsidis, M.W. Mahoney, P. Drineas, Unsupervised feature selection for principal components analysis, in: KDD'08: Proceeding of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2008, pp. 6169.
4. C. Boutsidis, M.W. Mahoney, P. Drineas, An improved approximation algorithm for the column subset selection problem, in: SODA'09: Proceedings of the 19th Annual ACMSIAM Symposium on Discrete Algorithms, 2009, pp. 968977.
5. A.M. Bruckstein, D.L. Donoho, and M. Elad From sparse solutions of systems of equations to sparse modeling of signals and images SIAM Review 51 1 2009 34 81
6. P.A. Businger, and G.H. Golub Linear least squares solutions by Householder transformations Numerische Mathematik 7 1965 269 276
7. T.F. Chan Rank revealing QR factorizations Linear Algebra and its Applications 88/89 1987 67 82
8. T.F. Chan, and P.C. Hansen Low-rank revealing QR factorizations Numerical Linear Algebra with Applications 1 1994 33 44
9. S. Chandrasekaran, and I.C.F. Ipsen On rank-revealing factorizations SIAM Journal on Matrix Analysis and Applications 15 1994 592 622
10. J. Chen, and X. Huo Theoretical results on sparse representations of multiple-measurement vectors IEEE Transactions on Signal Processing 54 2006 4634 4643 (Pubitemid 46405606)
11. G. Davis, S. Mallat, and M. Avellaneda Adaptive greedy approximations Constructive Approximation 13 1997 57 98
12. F.R. deHoog, and R.M.M. Mattheijb Subset selection for matrices Linear Algebra and its Applications 422 2007 349 359
13. A. Deshpande, K. Varadarajan, Sampling-based dimension reduction for subspace approximation, in: STOC'07: Proceedings of the 39th Annual ACM Aymposium on Theory of computing, 2007, pp. 641650. (Pubitemid 47630783)
14. A. Deshpande, S. Vempala, Adaptive sampling and fast low-rank matrix approximation, in: RANDOM'06: 10th International Workshop on Randomization and Computation, 2006, pp. 292303. (Pubitemid 44577539)
15. P. Drineas, A. Frieze, R. Kannan, S. Vempala, V. Vinay, Clustering in large graphs and matrices, in SODA'99: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete algorithms, 1999, pp. 291299.
16. P. Drineas, R. Kannan, and M.W. Mahoney Fast monte carlo algorithms for matrices II: computing a low-rank approximation to a matrix SIAM Journal on Computing 36 1 2006
17. P. Drineas, M.W. Mahoney, S. Muthukrishnan, Subspace sampling and relative-error matrix approximation: Column-based methods, in: RANDOM'06: 10th International Workshop on Randomization and Computation, 2006, pp. 316326. (Pubitemid 44577541)
18. P. Drineas, M.W. Mahoney, and S. Muthukrishnan Relative-error CUR matrix decompositions SIAM Journal on Matrix Analysis and Applications 30 2 2008 844 881
19. A. Frieze, R. Kannan, and S. Vempala Fast monte-carlo algorithms for finding low-rank approximations Journal of the ACM 51 6 2004
20. G.H. Golub, and C.H. Van Loan Matrix Computations 1996 Johns Hopkins U. Press
21. M. Gu, and S.C. Eisenstat Efficient algorithms for computing a strong rank-revealing QR factorization SIAM Journal on Scientific Computing 17 4 1996
22. V. Guruswami, A.K. Sinop, Optimal column-based low-rank matrix reconstruction. Manuscript, 2011.
23. Y.P. Hong, and C.T. Pan Rank-revealing QR factorizations and the singular value decomposition Mathematics of Computation 58 1992 213 232
24. W. Kahan Numerical linear algebra Canadian Mathematical Bulletin 9 1966 757 801
25. F.G. Kuruvilla, P.J. Park, and S.L. Schreiber Vector algebra in the analysis of genome-wide expression data Genome Biology 3 2002
26. A. Lutoborski, and V.N. Temlyakov Vector greedy algorithms Journal of Complexity 19 2003 458 473 (Pubitemid 36963754)
27. B.K. Natarajan Sparse approximate solutions to linear systems SIAM Journal on Computing 24 2 1995 227 234
28. C.T. Pan, and P.T.P. Tang Bounds on singular values revealed by QR factorizations BIT Numerical Mathematics 39 1999 740 756
29. M. Rudelson Random vectors in the isotropic position Journal of Functional Analysis 164 1 1999 60 72
30. M. Rudelson, and R. Vershynin Sampling from large matrices: an approach through geometric functional analysis Journal of the Association for Computing Machinery 54 4 2007
31. T. Sarlos, Improved approximation algorithms for large matrices via random projections. in: FOCS'06: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, 2006, pp. 143152. (Pubitemid 351175504)
32. N.D. Shyamalkumar, K. Varadarajan, Efficient subspace approximation algorithms in: SODA'07: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete algorithms, 2007, pp. 532540.
33. D.A. Spielman, and S.H. Teng Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time Journal of the ACM 51 3 2004 385 463
34. J.A. Tropp Greed is good: algorithmic results for sparse approximation IEEE Transactions on Information Theory 50 10 2004 2231 2242
35. J.A. Tropp, A.C. Gilbert, and M.J. Strauss Algorithms for simultaneous sparse approximation part I: Greedy pursuit Signal Processing 86 3 2006 572 588 (Pubitemid 43106572)