Faster SVD-truncated regularized least-squares

IEEE International Symposium on Information Theory - Proceedings

Volumn , Issue , 2014, Pages 1321-1325

  Boutsidis, Christos ^a   Magdon Ismail, Malik ^b  

^a YAHOO RESEARCH   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; INFORMATION THEORY;

FAST ALGORITHMS; HIGH PROBABILITY; K-MATRIX; LEAST SQUARE; SUBSPACE ITERATION METHOD;

ITERATIVE METHODS;

EID: 84906545975     PISSN: 21578095     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2014.6875047     Document Type: Conference Paper

References (18)

1. Y. S. Abu-Mostafa, M. Magdon-Ismail, and H.-T. Lin. Learning from data. AMLBook, 2012.
2. C. Boutsidis and M. Magdon-Ismail. A note on sparse least-squares regression. Information Processing Letters, 2013.
3. T. F. Chan and P. C. Hansen. Some applications of the rank revealing QR factorization. SIAM Journal on Scientific and Statistical Computing, 13:727-741, 1992.
4. K. R. Davidson and S. J. Szarek. Local Operator Theory, Random Matrices and Banach Spaces. In Handbook of the Geometry of Banach Spaces, volume 1. Elsevier Science, 2001.
5. A. Gittens, P. Kambadur, and C. Boutsidis. Approximate spectral clustering via randomized sketching. preprint arXiv:1311.2854, 2013.
6. G. Golub and C. Van Loan. Matrix computations. JHU Press, 2012.
7. M. Gu and S. Eisenstat. Efficient algorithms for computing a strong rank-revealing QR factorization. SIAM Journal on Scientific Computing, 17:848-869, 1996.
8. N. Halko, P.-G. Martinsson, and J. A. Tropp. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions. SIAM review, 53(2):217-288, 2011.
9. P. Hansen. The truncated SVD as a method for regularization. BIT Numerical Mathematics, 27(4):534-553, 1987.
10. P. C. Hansen. Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. SIAM Journal on Scientific and Statistical Computing, 11(3):503-518, 1990.
11. R. Horn and C. Johnson. Matrix Analysis. CUP, NY, 1985.
12. D. P. O'Leary and J. A. Simmons. A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems. SIAM Journal on Scientific and Statistical Computing, 2(4):474-489, 1981.
13. V. Rokhlin, A. Szlam, and M. Tygert. A randomized algorithm for principal component analysis. SIAM Journal on Matrix Analysis and Applications, 31(3):1100-1124, 2009.
14. A. Sankar, D. A. Spielman, and S.-H. Teng. Smoothed analysis of the condition numbers and growth factors of matrices. SIAM Journal on Matrix Analysis and Applications, 28(2):446-476, 2006.
15. G. Stewart. On the perturbation of pseudo-inverses, projections and linear least squares problems. SIAM review, 19(4):634-662, 1977.
16. J. M. Varah. On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems. SIAM Journal on Numerical Analysis, 10(2):257-267, 1973.
17. C. Vogel and J. Wade. Iterative SVD-based methods for ill-posed problems. SIAM Journal on Scientific Computing, 15(3):736-754, 1994.
18. H. Xiang and J. Zou. Regularization with randomized SVD for largescale discrete inverse problems. Inverse Problems, 29(8):085008, 2013.