메뉴 건너뛰기




Volumn , Issue , 2014, Pages 353-362

Optimal CUR matrix decompositions

Author keywords

Adaptive sampling; Column subset selection; CUR; Input sparsity tim; Leverage scores; Low rank matrix decomposition; Spectral sparsification; SVD

Indexed keywords

ALGORITHMS; CURING; SINGULAR VALUE DECOMPOSITION;

EID: 84904285267     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2591796.2591819     Document Type: Conference Paper
Times cited : (73)

References (47)
  • 2
    • 0038166193 scopus 로고    scopus 로고
    • Database-friendly random projections: Johnson-lindenstrauss with binary coins
    • D. Achlioptas, "Database-friendly random projections: Johnson-lindenstrauss with binary coins," J. Comput. Syst. Sci., vol. 66, no. 4, pp. 671-687, 2003.
    • (2003) J. Comput. Syst. Sci. , vol.66 , Issue.4 , pp. 671-687
    • Achlioptas, D.1
  • 4
    • 30544452185 scopus 로고    scopus 로고
    • Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices
    • M. W. Berry, S. A. Pulatova, and G. Stewart, "Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices," ACM Transactions on Mathematical Software (TOMS), vol. 31, no. 2, pp. 252-269, 2005.
    • (2005) ACMTransactions on Mathematical Software (TOMS) , vol.31 , Issue.2 , pp. 252-269
    • Berry, M.W.1    Pulatova, S.A.2    Stewart, G.3
  • 9
    • 84879805132 scopus 로고    scopus 로고
    • Low rank approximation and regression in input sparsity time
    • K. L. Clarkson and D. P. Woodruff, "Low rank approximation and regression in input sparsity time," in In STOC, 2013.
    • (2013) STOC
    • Clarkson, K.L.1    Woodruff, D.P.2
  • 13
    • 51849141693 scopus 로고    scopus 로고
    • Adaptive sampling and fast low-rank matrix approximation
    • A. Deshpande and S. Vempala, "Adaptive sampling and fast low-rank matrix approximation," in RANDOM - APPROX, 2006.
    • (2006) Random - Approx
    • Deshpande, A.1    Vempala, S.2
  • 15
    • 0038416092 scopus 로고    scopus 로고
    • Pass efficient algorithms for approximating large matrices
    • -, vPass efficient algorithms for approximating large matrices," in SODA, 2003, pp. 223-232.
    • (2003) SODA , pp. 223-232
    • Drineas, P.1    Kannan, R.2
  • 16
    • 33751115359 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication
    • P. Drineas, R. Kannan, and M. Mahoney, "Fast Monte Carlo algorithms for matrices I: Approximating matrix multiplication," SIAM Journal of Computing, vol. 36, no. 1, pp. 132-157, 2006.
    • (2006) SIAMJournal of Computing , vol.36 , Issue.1 , pp. 132-157
    • Drineas, P.1    Kannan, R.2    Mahoney, M.3
  • 17
    • 33751075906 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix
    • -, "Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix," SIAM Journal of Computing, vol. 36, no. 1, pp. 158-183, 2006.
    • (2006) SIAMJournal of Computing , vol.36 , Issue.1 , pp. 158-183
    • Drineas, P.1    Kannan, R.2    Mahoney, M.3
  • 18
    • 33751097630 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition
    • -, "Fast Monte Carlo algorithms for matrices III: Computing a compressed approximate matrix decomposition," SIAM Journal of Computing, vol. 36, no. 1, pp. 184-206, 2006.
    • (2006) SIAMJournal of Computing , vol.36 , Issue.1 , pp. 184-206
    • Drineas, P.1    Kannan, R.2    Mahoney, M.3
  • 20
    • 33750038332 scopus 로고    scopus 로고
    • Polynomial time algorithm for column-row based relative-error low-rank matrix approximation
    • March
    • P. Drineas, M. Mahoney, and S. Muthukrishnan, "Polynomial time algorithm for column-row based relative-error low-rank matrix approximation," DIMACS, Tech. Rep. 2006-04, March 2006.
    • (2006) DIMACS, Tech. Rep 2006-04
    • Drineas, P.1    Mahoney, M.2    Muthukrishnan, S.3
  • 21
    • 29244453931 scopus 로고    scopus 로고
    • On the nyström method for approximating a gram matrix for improved kernel-based learning
    • P. Drineas and M. W. Mahoney, "On the nyström method for approximating a gram matrix for improved kernel-based learning," The Journal of Machine Learning Research, vol. 6, pp. 2153-2175, 2005.
    • (2005) The Journal of Machine Learning Research , vol.6 , pp. 2153-2175
    • Drineas, P.1    Mahoney, M.W.2
  • 26
    • 27544513989 scopus 로고    scopus 로고
    • Pseudo-skeleton approximations by matrices of maximal volume
    • S. Goreinov, N. Zamarashkin, and E. Tyrtyshnikov, "Pseudo-skeleton approximations by matrices of maximal volume," Mathematical Notes, vol. 62, no. 4, pp. 515-519, 1997.
    • (1997) Mathematical Notes , vol.62 , Issue.4 , pp. 515-519
    • Goreinov, S.1    Zamarashkin, N.2    Tyrtyshnikov, E.3
  • 29
    • 79960425522 scopus 로고    scopus 로고
    • Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
    • N. Halko, P. Martinsson, and J. Tropp, "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," SIAM Review, vol. 53, no. 2, p. 217-288, 2011.
    • (2011) SIAMReview , vol.53 , Issue.2 , pp. 217-288
    • Halko, N.1    Martinsson, P.2    Tropp, J.3
  • 30
    • 0005540367 scopus 로고    scopus 로고
    • Improved bound for rank revealing LU factorizations
    • T. Hwang, W. Lin, and D. Pierce, "Improved bound for rank revealing LU factorizations," Linear algebra and its applications, vol. 261, no. 1-3, pp. 173-186, 1997.
    • (1997) Linear Algebra and Its Applications , vol.261 , Issue.1-3 , pp. 173-186
    • Hwang, T.1    Lin, W.2    Pierce, D.3
  • 35
    • 84879805212 scopus 로고    scopus 로고
    • Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
    • X. Meng and M. W. Mahoney, "Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression," in In STOC. ACM, 2013, pp. 91-100.
    • (2013) STOC ACM , pp. 91-100
    • Meng, X.1    Mahoney, M.W.2
  • 37
    • 84893239024 scopus 로고    scopus 로고
    • Osnap: Faster numerical linear algebra algorithms via sparser subspace embeddings
    • J. Nelson and H. L. Nguyên, "Osnap: Faster numerical linear algebra algorithms via sparser subspace embeddings," in In FOCS, 2013.
    • (2013) FOCS
    • Nelson, J.1    Nguyên, H.L.2
  • 38
    • 0034392123 scopus 로고    scopus 로고
    • On the existence and computation of rank-revealing LU factorizations
    • C. Pan, "On the existence and computation of rank-revealing LU factorizations," Linear Algebra and its Applications, vol. 316, no. 1-3, pp. 199-222, 2000.
    • (2000) Linear Algebra and Its Applications , vol.316 , Issue.1-3 , pp. 199-222
    • Pan, C.1
  • 39
    • 51649090940 scopus 로고    scopus 로고
    • A fast randomized algorithm for overdetermined linear least-squares regression
    • V. Rokhlin and M. Tygert, "A fast randomized algorithm for overdetermined linear least-squares regression," Proceedings of the National Academy of Sciences, vol. 105, no. 36, p. 13212, 2008.
    • (2008) Proceedings of the National Academy of Sciences , vol.105 , Issue.36 , pp. 13212
    • Rokhlin, V.1    Tygert, M.2
  • 40
    • 34547728320 scopus 로고    scopus 로고
    • Sampling from large matrices: An approach through geometric functional analysis
    • M. Rudelson and R. Vershynin, "Sampling from large matrices: An approach through geometric functional analysis," JACM: Journal of the ACM, vol. 54, 2007.
    • (2007) JACM Journal of the ACM , vol.54
    • Rudelson, M.1    Vershynin, R.2
  • 42
    • 84857121407 scopus 로고    scopus 로고
    • On generalized matrix approximation problem in the spectral norm
    • K. C. Sou and A. Ranzer, "On generalized matrix approximation problem in the spectral norm," Linear Algebra and its Applications, vol. 436, no. 7, pp. 2331-2341, 2012.
    • (2012) Linear Algebra and Its Applications , vol.436 , Issue.7 , pp. 2331-2341
    • Sou, K.C.1    Ranzer, A.2
  • 43
    • 0040117178 scopus 로고    scopus 로고
    • Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix
    • G. Stewart, "Four algorithms for the efficient computation of truncated QR approximations to a sparse matrix," Numerische Mathematik, vol. 83, pp. 313-323, 1999.
    • (1999) Numerische Mathematik , vol.83 , pp. 313-323
    • Stewart, G.1
  • 44
    • 0029692981 scopus 로고    scopus 로고
    • Mosaic-skeleton approximations
    • E. Tyrtyshnikov, "Mosaic-skeleton approximations," Calcolo, vol. 33, no. 1, pp. 47-57, 1996.
    • (1996) Calcolo , vol.33 , Issue.1 , pp. 47-57
    • Tyrtyshnikov, E.1
  • 45
    • 0038805356 scopus 로고    scopus 로고
    • Incomplete cross approximation in the mosaic-skeleton method
    • -, "Incomplete cross approximation in the mosaic-skeleton method," Computing, vol. 64, no. 4, pp. 367-380, 2000.
    • (2000) Computing , vol.64 , Issue.4 , pp. 367-380
    • Tyrtyshnikov, E.1
  • 46
    • 84885649693 scopus 로고    scopus 로고
    • Improving cur matrix decomposition and the nystrom approximation via adaptive sampling
    • S. Wang and Z. Zhang, "Improving cur matrix decomposition and the nystrom approximation via adaptive sampling," Journal of Machine Learning Research, 2013.
    • (2013) Journal of Machine Learning Research
    • Wang, S.1    Zhang, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.