-
1
-
-
0034830284
-
Fast computation of low rank matrix approximations
-
New York
-
D. ACHLIOPTAS AND F. MCSHERRY, Fast computation of low rank matrix approximations, in Proceedings of the Thirty-Third Annual Symposium on Theory of Computing, ACM, New York, 2001, pp. 611-618.
-
(2001)
Proceedings of the Thirty-Third Annual Symposium on Theory of Computing, ACM
, pp. 611-618
-
-
Achlioptas, D.1
McSherry, F.2
-
2
-
-
34247228045
-
Fast computation of low-rank matrix approximations
-
article
-
D. ACHLIOPTAS AND F. MCSHERRY, Fast computation of low-rank matrix approximations, J. ACM, 54 (2007), article 9.
-
(2007)
J. ACM
, vol.54
, pp. 9
-
-
Achlioptas, D.1
McSherry, F.2
-
3
-
-
0001326391
-
Some applications of the rank revealing QR factorization
-
T. F. CHAN AND P. C. HANSEN, Some applications of the rank revealing QR factorization, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 727-741.
-
(1992)
SIAM J. Sci. Statist. Comput.
, vol.13
, pp. 727-741
-
-
Chan, T.F.1
Hansen, P.C.2
-
4
-
-
33746136466
-
Condition numbers of gaussian random matrices
-
Z. CHEN AND J. J. DONGARRA, Condition numbers of Gaussian random matrices, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 603-620.
-
(2005)
SIAM J. Matrix Anal. Appl.
, vol.27
, pp. 603-620
-
-
Chen, Z.1
Dongarra, J.J.2
-
5
-
-
70350688128
-
Numerical linear algebra in the streaming model
-
New York
-
K. L. CLARKSON AND D. P. WOODRUFF, Numerical linear algebra in the streaming model, in Proceedings of the 41st Annual ACM Symposium on Theory of Computing, ACM, New York, 2009, pp. 205-214.
-
(2009)
Proceedings of the 41st Annual ACM Symposium on Theory of Computing, ACM
, pp. 205-214
-
-
Clarkson, K.L.1
Woodruff, D.P.2
-
6
-
-
84989525001
-
Indexing by latent semantic analysis
-
S. DEERWESTER, S. T. DUMAIS, G. W. FURNAS, T. K. LANDAUER, AND R. HARSHMAN, Indexing by latent semantic analysis, J. Amer. Soc. Inform. Sci., 41 (1990), pp. 391-407.
-
(1990)
J. Amer. Soc. Inform. Sci.
, vol.41
, pp. 391-407
-
-
Deerwester, S.1
Dumais, S.T.2
Furnas, G.W.3
Landauer, T.K.4
Harshman, R.5
-
7
-
-
33244455701
-
Matrix approximation and projective clustering via volume sampling
-
New York
-
A. DESHPANDE, L. RADEMACHER, S. VEMPALA, AND G. WANG, Matrix approximation and projective clustering via volume sampling, in Proceedings of the Seventeenth ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 2006, pp. 1117-1126.
-
(2006)
Proceedings of the Seventeenth ACM-SIAM Symposium on Discrete Algorithms, ACM
, pp. 1117-1126
-
-
Deshpande, A.1
Rademacher, L.2
Vempala, S.3
Wang, G.4
-
8
-
-
33750065382
-
Adaptive sampling and fast low-rank matrix approximation
-
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a
-
A. DESHPANDE AND S. VEMPALA, Adaptive sampling and fast low-rank matrix approximation, Lecture Notes in Comput. Sci. 4110, Springer, Berlin, 2006, pp. 292-303. (Pubitemid 44577539)
-
(2006)
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
, vol.4110
, pp. 292-303
-
-
Deshpande, A.1
Vempala, S.2
-
9
-
-
0001290746
-
Estimating extremal eigenvalues and condition numbers of matrices
-
J. D. DIXON, Estimating extremal eigenvalues and condition numbers of matrices, SIAM J. Numer. Anal., 20 (1983), pp. 812-814.
-
(1983)
SIAM J. Numer. Anal.
, vol.20
, pp. 812-814
-
-
Dixon, J.D.1
-
10
-
-
35248881205
-
An experimental evaluation of a monte-carlo algorithm for singular value decomposition
-
Y. Manolopoulos, S. Evripidou, and A. C. Kakas, eds., Springer, Berlin
-
P. DRINEAS, E. DRINEA, AND P. S. HUGGINS, An experimental evaluation of a Monte-Carlo algorithm for singular value decomposition, in Revised Selected Papers from the Eighth Panhellenic Conference on Informatics, Lecture Notes in Comput. Sci. 2563, Y. Manolopoulos, S. Evripidou, and A. C. Kakas, eds., Springer, Berlin, 2003, pp. 279-296.
-
(2003)
Revised Selected Papers from the Eighth Panhellenic Conference on Informatics, Lecture Notes in Comput. Sci.
, vol.2563
, pp. 279-296
-
-
Drineas, P.1
Drinea, E.2
Huggins, P.S.3
-
11
-
-
33751075906
-
Fast monte carlo algorithms for matrices. II
-
P. DRINEAS, R. KANNAN, AND M. W. MAHONEY, Fast Monte Carlo algorithms for matrices. II. Computing a low-rank approximation to a matrix, SIAM J. Comput., 36 (2006), pp. 158- 183.
-
(2006)
Computing a low-rank approximation to a matrix, SIAM J. Comput.
, vol.36
, pp. 158-183
-
-
Drineas, P.1
Kannan, R.2
Mahoney, M.W.3
-
12
-
-
33751097630
-
Fast monte carlo algorithms for matrices. III
-
P. DRINEAS, R. KANNAN, AND M. W. MAHONEY, Fast Monte Carlo algorithms for matrices. III. Computing a compressed approximate matrix decomposition, SIAM J. Comput., 36 (2006), pp. 184-206.
-
(2006)
Computing a Compressed Approximate Matrix Decomposition, Siam J. Comput.
, vol.36
, pp. 184-206
-
-
Drineas, P.1
Kannan, R.2
Mahoney, M.W.3
-
13
-
-
33750038332
-
-
Technical report 2006-04, DIMACS, Piscataway, NJ
-
P. DRINEAS, M. W. MAHONEY, AND S. MUTHUKRISHNAN, Polynomial Time Algorithm for Column-Row-Based Relative-Error Low-Rank Matrix Approximation, Technical report 2006-04, DIMACS, Piscataway, NJ, 2006.
-
(2006)
Polynomial Time Algorithm for Column-Row-Based Relative-Error Low-Rank Matrix Approximation
-
-
Drineas, P.1
Mahoney, M.W.2
Muthukrishnan, S.3
-
14
-
-
58849107202
-
Relative-error CUR matrix decompositions
-
P. DRINEAS, M. W. MAHONEY, AND S. MUTHUKRISHNAN, Relative-error CUR matrix decompositions, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 844-881.
-
(2008)
SIAM J. Matrix Anal. Appl.
, vol.30
, pp. 844-881
-
-
Drineas, P.1
Mahoney, M.W.2
Muthukrishnan, S.3
-
15
-
-
33845962871
-
Fast monte-carlo low rank approximations for matrices
-
S. FRIEDLAND, M. KAVEH, A. NIKNEJAD, AND H. ZARE, Fast Monte-Carlo low rank approximations for matrices, in Proceedings of the First IEEE International Conference on System of Systems Engineering (SoSE 2006), Los Angeles, 2006, pp. 218-223.
-
(2006)
Proceedings of the First IEEE International Conference on System of Systems Engineering (SoSE 2006), Los Angeles
, pp. 218-223
-
-
Friedland, S.1
Kaveh, M.2
Niknejad, A.3
Zare, H.4
-
16
-
-
0040942625
-
Quick approximation to matrices and applications
-
A. FRIEZE AND R. KANNAN, Quick approximation to matrices and applications, Combinatorica, 19 (1999), pp. 175-220.
-
(1999)
Combinatorica
, vol.19
, pp. 175-220
-
-
Frieze, A.1
Kannan, R.2
-
17
-
-
0032308232
-
Fast monte-carlo algorithms for finding low-rank approximations
-
New York
-
A. FRIEZE, R. KANNAN, AND S. VEMPALA, Fast Monte-Carlo algorithms for finding low-rank approximations, in Proceedings of the Thirty-Ninth Annual IEEE Symposium on Foundations of Computer Science, ACM, New York, 1998, pp. 370-378.
-
(1998)
Proceedings of the Thirty-Ninth Annual IEEE Symposium on Foundations of Computer Science, ACM
, pp. 370-378
-
-
Frieze, A.1
Kannan, R.2
Vempala, S.3
-
18
-
-
20444476106
-
Fast monte-carlo algorithms for finding low-rank approximations
-
A. FRIEZE, R. KANNAN, AND S. VEMPALA, Fast Monte-Carlo algorithms for finding low-rank approximations, J. ACM, 51 (2004), pp. 1025-1041.
-
(2004)
J. ACM
, vol.51
, pp. 1025-1041
-
-
Frieze, A.1
Kannan, R.2
Vempala, S.3
-
19
-
-
84968515320
-
Numerical inverting of matrices of high order
-
H. H. GOLDSTINE AND J. VON NEUMANN, Numerical inverting of matrices of high order, II, Proc. Amer. Math. Soc., 2 (1951), pp. 188-202.
-
(1951)
II, Proc. Amer. Math. Soc.
, vol.2
, pp. 188-202
-
-
Goldstine, H.H.1
Von Neumann, J.2
-
20
-
-
0004236492
-
-
3rd ed., Johns Hopkins University Press, Baltimore, MD
-
G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
-
(1996)
Matrix Computations
-
-
Golub, G.H.1
Van Loan, C.F.2
-
21
-
-
0037790752
-
The maximal-volume concept in approximation by low-rank matrices
-
University of Colorado, Boulder, 1999, V. Olshevsky, ed., Contemp. Math. 280, AMS, Providence
-
S. A. GOREINOV AND E. E. TYRTYSHNIKOV, The Maximal-Volume Concept in Approximation by Low-Rank Matrices, in Structured Matrices in Mathematics, Computer Science, and Engineering, I, Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder, 1999, V. Olshevsky, ed., Contemp. Math. 280, AMS, Providence, RI, 2001, pp. 47-51.
-
(2001)
Structured Matrices in Mathematics, Computer Science, and Engineering, I, Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference
, vol.RI
, pp. 47-51
-
-
Goreinov, S.A.1
Tyrtyshnikov, E.E.2
-
22
-
-
27544513989
-
Pseudo-skeleton approximations by matrices of maximal volume
-
S. A. GOREINOV, E. E. TYRTYSHNIKOV, AND N. L. ZAMARASHKIN, Pseudo-skeleton approximations by matrices of maximal volume, Math. Notes, 62 (1997), pp. 515-519.
-
(1997)
Math. Notes
, vol.62
, pp. 515-519
-
-
Goreinov, S.A.1
Tyrtyshnikov, E.E.2
Zamarashkin, N.L.3
-
23
-
-
0039506183
-
A theory of pseudoskeleton approximations
-
S. A. GOREINOV, E. E. TYRTYSHNIKOV, AND N. L. ZAMARASHKIN, A theory of pseudoskeleton approximations, Linear Algebra Appl., 261 (1997), pp. 1-21.
-
(1997)
Linear Algebra Appl.
, vol.261
, pp. 1-21
-
-
Goreinov, S.A.1
Tyrtyshnikov, E.E.2
Zamarashkin, N.L.3
-
24
-
-
0003216822
-
Efficient algorithms for computing a strong rank-revealing QR factorization
-
M. GU AND S. C. EISENSTAT, Efficient algorithms for computing a strong rank-revealing QR factorization, SIAM J. Sci. Comput., 17 (1996), pp. 848-869.
-
(1996)
SIAM J. Sci. Comput.
, vol.17
, pp. 848-869
-
-
Gu, M.1
Eisenstat, S.C.2
-
26
-
-
0043178250
-
Estimating the largest eigenvalue by the power and lanczos algorithms with a random start
-
J. KUCZYŃSKI AND H. WOŹNIAKOWSKI, Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 1094- 1122.
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 1094-1122
-
-
Kuczyński, J.1
Woźniakowski, H.2
-
27
-
-
38049173092
-
Randomized algorithms for the low-rank approximation of matrices
-
E. LIBERTY, F. WOOLFE, P.-G. MARTINSSON, V. ROKHLIN, AND M. TYGERT, Randomized algorithms for the low-rank approximation of matrices, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 20167-20172.
-
(2007)
Proc. Natl. Acad. Sci. USA
, vol.104
, pp. 20167-20172
-
-
Liberty, E.1
Woolfe, F.2
Martinsson, P.-G.3
Rokhlin, V.4
Tygert, M.5
-
28
-
-
58849086813
-
CUR matrix decompositions for improved data analysis
-
M. W. MAHONEY AND P. DRINEAS, CUR matrix decompositions for improved data analysis, Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 697-702.
-
(2009)
Proc. Natl. Acad. Sci. USA
, vol.106
, pp. 697-702
-
-
Mahoney, M.W.1
Drineas, P.2
-
29
-
-
38049187128
-
-
Technical report 1361, Yale University, Department of Computer Science, New Haven, CT, 2006. Available in the form referenced in the present paper at
-
P.-G. MARTINSSON, V. ROKHLIN, AND M. TYGERT, A Randomized Algorithm for the Approximation of Matrices, Technical report 1361, Yale University, Department of Computer Science, New Haven, CT, 2006. Available in the form referenced in the present paper at http://www.cs.yale.edu/publications/ techreports/tr1361.pdf and in revised form (with renumbered lemmas) at http://www.cs.yale.edu/~tygert/randapp.pdf.
-
A Randomized Algorithm for the Approximation of Matrices
-
-
Martinsson, P.-G.1
Rokhlin, V.2
Tygert, M.3
-
30
-
-
0034297382
-
Latent semantic indexing: A probabilistic analysis
-
C. H. PAPADIMITRIOU, P. RAGHAVAN, H. TAMAKI, AND S. VEMPALA, Latent semantic indexing: A probabilistic analysis, J. Comput. System Sci., 61 (2000), pp. 217-235.
-
(2000)
J. Comput. System Sci.
, vol.61
, pp. 217-235
-
-
Papadimitriou, C.H.1
Raghavan, P.2
Tamaki, H.3
Vempala, S.4
-
31
-
-
84898929664
-
EM algorithms for PCA and SPCA
-
MIT Press, Cambridge, MA
-
S. ROWEIS, EM algorithms for PCA and SPCA, in Proceedings of the 1997 Conference on Advances in Neural Information Processing Systems 10, MIT Press, Cambridge, MA, 1998, pp. 626-632.
-
(1998)
Proceedings of the 1997 Conference on Advances in Neural Information Processing Systems
, vol.10
, pp. 626-632
-
-
Roweis, S.1
-
32
-
-
35348901208
-
Improved approximation algorithms for large matrices via random projections
-
Berkeley, CA, IEEE Computer Society, Washington, D.C.
-
T. SARLÓS, Improved approximation algorithms for large matrices via random projections, in Proceedings of the Forty-Seventh Annual IEEE Symposium on Foundations of Computer Science, Berkeley, CA, IEEE Computer Society, Washington, D.C., 2006, pp. 143-152.
-
(2006)
Proceedings of the Forty-Seventh Annual IEEE Symposium on Foundations of Computer Science
, pp. 143-152
-
-
Sarlós, T.1
-
33
-
-
72449121227
-
-
Technical report, Eötvös Loránd University, Informatics Laboratory, Budapest, Hungary, Available online at
-
T. SARLÓS, Improved Approximation Algorithms for Large Matrices via Random Projections, Long Form, Technical report, Eötvös Loránd University, Informatics Laboratory, Budapest, Hungary, 2006. Available online at http://www.ilab.sztaki.hu/~stamas/publications/rplong. pdf.
-
(2006)
Improved Approximation Algorithms for Large Matrices via Random Projections, Long Form
-
-
Sarlós, T.1
-
34
-
-
48349138074
-
Less is more: Compact matrix decomposition for large sparse graphs
-
J. SUN, Y. XIE, H. ZHANG, AND C. FALOUTSOS, Less is more: Compact matrix decomposition for large sparse graphs, Stat. Anal. Data Min., 1 (2008), pp. 6-22.
-
(2008)
Stat. Anal. Data Min.
, vol.1
, pp. 6-22
-
-
Sun, J.1
Xie, Y.2
Zhang, H.3
Faloutsos, C.4
-
35
-
-
0038805356
-
Incomplete cross approximation in the mosaic-skeleton method
-
E. E. TYRTYSHNIKOV, Incomplete cross approximation in the mosaic-skeleton method, Computing, 64 (2000), pp. 367-380.
-
(2000)
Computing
, vol.64
, pp. 367-380
-
-
Tyrtyshnikov, E.E.1
-
37
-
-
53049094679
-
A fast randomized algorithm for the approximation of matrices
-
F. WOOLFE, E. LIBERTY, V. ROKHLIN, AND M. TYGERT, A fast randomized algorithm for the approximation of matrices, Appl. Comput. Harmon. Anal., 25 (2008), pp. 335-366.
-
(2008)
Appl. Comput. Harmon. Anal.
, vol.25
, pp. 335-366
-
-
Woolfe, F.1
Liberty, E.2
Rokhlin, V.3
Tygert, M.4
|