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Volumn 13, Issue , 2012, Pages 3441-3473

Iterative reweighted algorithms for matrix rank minimization

Author keywords

Iterative algorithms; Matrix completion; Matrix rankminimization; Null space property

Indexed keywords

AFFINE CONSTRAINTS; COMPUTATIONALLY EFFICIENT; DATA SETS; EFFICIENT IMPLEMENTATION; EMPIRICAL PERFORMANCE; ITERATIVE ALGORITHM; ITERATIVE RE-WEIGHTED LEAST SQUARES ALGORITHMS; LOW-RANK MATRICES; MATRIX COMPLETION; MATRIX COMPLETION PROBLEMS; MATRIX RANK; MINIMUM RANK; NP-HARD; NULL-SPACE PROPERTY; RANDOM INSTANCE; RANK FUNCTIONS; SMOOTH APPROXIMATION; TRACE-NORMS;

EID: 84870936812     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (381)

References (49)
  • 4
    • 77951291046 scopus 로고    scopus 로고
    • A singular value thresholding algorithm for matrix completion
    • J.F. Cai, E.J. Candes, and Z. Shen. A singular value thresholding algorithm for matrix completion. SIAM J. On Optimization, 20(4):1956-1982, 2008.
    • (2008) SIAM J. On Optimization , vol.20 , Issue.4 , pp. 1956-1982
    • Cai, J.F.1    Candes, E.J.2    Shen, Z.3
  • 13
    • 44449127493 scopus 로고    scopus 로고
    • Restricted isometry properties and nonconvex compressive sensing
    • 035020
    • R. Chartrand and V. Staneva. Restricted isometry properties and nonconvex compressive sensing. Inverse Problems, 24(035020):1-14, 2008.
    • (2008) Inverse Problems , vol.24 , pp. 1-14
    • Chartrand, R.1    Staneva, V.2
  • 15
    • 77949704355 scopus 로고    scopus 로고
    • Iteratively re-weighted least squares minimization for sparse recovery
    • I. Daubechies, R. DeVore, M. Fornasier, and C.S. Gunturk. Iteratively re-weighted least squares minimization for sparse recovery. Commun. Pure Appl. Math, 63(1):1-38, 2010.
    • (2010) Commun. Pure Appl. Math , vol.63 , Issue.1 , pp. 1-38
    • Daubechies, I.1    DeVore, R.2    Fornasier, M.3    Gunturk, C.S.4
  • 16
    • 33751075906 scopus 로고    scopus 로고
    • Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix
    • DOI 10.1137/S0097539704442696
    • P. Drineas, R. Kannan, andM.W.Mahoney. Fast monte carlo algorithms for matrices ii: Computing a low rank approximation to a matrix. SIAM Journal on Computing, 36:158-183, 2006. (Pubitemid 46374022)
    • (2006) SIAM Journal on Computing , vol.36 , Issue.1 , pp. 158-183
    • Drineas, P.1    Kannan, R.2    Mahoney, M.W.3
  • 17
    • 0034853839 scopus 로고    scopus 로고
    • A rank minimization heuristic with application to minimum order system approximation
    • Arlington, VA
    • M. Fazel, H. Hindi, and S. Boyd. A rank minimization heuristic with application to minimum order system approximation. In Proc. American Control Conference, Arlington, VA, 2001.
    • (2001) Proc. American Control Conference
    • Fazel, M.1    Hindi, H.2    Boyd, S.3
  • 18
    • 0142215333 scopus 로고    scopus 로고
    • Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices
    • Denver, CO
    • M. Fazel, H. Hindi, and S. Boyd. Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices. In Proc. American Control Conference, pages 2156-2162, Denver, CO, 2003.
    • (2003) Proc. American Control Conference , pp. 2156-2162
    • Fazel, M.1    Hindi, H.2    Boyd, S.3
  • 19
    • 84856046837 scopus 로고    scopus 로고
    • Low-rank matrix recovery via iteratively reweighted least squares minimization
    • M. Fornasier, H. Rauhut, and R. Ward. Low-rank matrix recovery via iteratively reweighted least squares minimization. SIAM Journal of Optimization, 21(4), 2011.
    • (2011) SIAM Journal of Optimization , vol.21 , Issue.4
    • Fornasier, M.1    Rauhut, H.2    Ward, R.3
  • 21
    • 71149117997 scopus 로고    scopus 로고
    • Gradient descent with sparsification: An iterative algorithm for sparse recovery with restricted isometry property
    • R. Garg and R. Khandekar. Gradient descent with sparsification: An iterative algorithm for sparse recovery with restricted isometry property. In Proc. Of 26th Intl. Conf. On Machine Learning (ICML), 2009.
    • (2009) Proc. Of 26th Intl. Conf. On Machine Learning (ICML)
    • Garg, R.1    Khandekar, R.2
  • 22
    • 79952483985 scopus 로고    scopus 로고
    • Convergence of fixed point continuation algorithms for matrix rank minimization
    • D. Goldfarb and S. Ma. Convergence of fixed point continuation algorithms for matrix rank minimization. Foundations of Computational Mathematics, 11(2), 2011.
    • (2011) Foundations of Computational Mathematics , vol.11 , Issue.2
    • Goldfarb, D.1    Ma, S.2
  • 23
    • 84870876408 scopus 로고    scopus 로고
    • Available at
    • D. Goldfarb and S. Ma. FPCA code. 2009. Available at http://www.columbia. edu/?sm2756/FPCA.htm.
    • (2009) FPCA Code
    • Goldfarb, D.1    Ma, S.2
  • 25
    • 79960425522 scopus 로고    scopus 로고
    • Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions
    • N. Halko, P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions. SIAM Review, 53(2):217-288, 2011.
    • (2011) SIAM Review , vol.53 , Issue.2 , pp. 217-288
    • Halko, N.1    Martinsson, P.G.2    Tropp, J.A.3
  • 31
    • 77955747588 scopus 로고    scopus 로고
    • Admira: Atomic decomposition for minimum rank approximation
    • K. Lee and Y. Bresler. Admira: Atomic decomposition for minimum rank approximation. IEEE Tran. Info. Theory, 56(9), 2010.
    • (2010) IEEE Tran. Info. Theory , vol.56 , Issue.9
    • Lee, K.1    Bresler, Y.2
  • 32
    • 0030205038 scopus 로고    scopus 로고
    • Derivatives of spectral functions
    • A.S. Lewis. Derivatives of spectral functions. Mathematics of Operations Research, 21(3):576-588, 1996.
    • (1996) Mathematics of Operations Research , vol.21 , Issue.3 , pp. 576-588
    • Lewis, A.S.1
  • 33
    • 72549110327 scopus 로고    scopus 로고
    • Interior-point method for nuclear norm approximation with application to system identification
    • Z. Liu and L. Vandenberghe. Interior-point method for nuclear norm approximation with application to system identification. SIAM J. Matrix Analysis and Appl., 31(3), 2008.
    • (2008) SIAM J. Matrix Analysis and Appl , vol.31 , Issue.3
    • Liu, Z.1    Vandenberghe, L.2
  • 34
    • 33847366224 scopus 로고    scopus 로고
    • Portfolio optimization with linear and fixed transaction costs
    • M. S. Lobo, M. Fazel, and S. Boyd. Portfolio optimization with linear and fixed transaction costs. Annals of Operations Research, 152:341-365, 2006.
    • (2006) Annals of Operations Research , vol.152 , pp. 341-365
    • Lobo, M.S.1    Fazel, M.2    Boyd, S.3
  • 36
    • 77956944781 scopus 로고    scopus 로고
    • Spectral regularization algorithms for learning large incomplete matrices
    • R. Mazumder, T. Hastie, and R. Tibshirani. Spectral regularization algorithms for learning large incomplete matrices. Journal of Machine Learning Research, 11:2287 -2322, 2010.
    • (2010) Journal of Machine Learning Research , vol.11 , pp. 2287-2322
    • Mazumder, R.1    Hastie, T.2    Tibshirani, R.3
  • 38
    • 77957812855 scopus 로고    scopus 로고
    • Reweighted nuclear norm minimization with application to system identification
    • Baltimore, MA
    • K. Mohan and M. Fazel. Reweighted nuclear norm minimization with application to system identification. In Proc. American Control Conference, Baltimore, MA, 2010a.
    • (2010) Proc. American Control Conference
    • Mohan, K.1    Fazel, M.2
  • 41
    • 62749175137 scopus 로고    scopus 로고
    • Cosamp: Iterative signal recovery from incomplete and inaccurate samples
    • D. Needell and J. A. Tropp. Cosamp: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3):301-321, 2008.
    • (2008) Applied and Computational Harmonic Analysis , vol.26 , Issue.3 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 46
    • 84863072011 scopus 로고    scopus 로고
    • Face recovery in conference video streaming using robust principal component analysis
    • W. Tan, G. Cheung, and Y. Ma. Face recovery in conference video streaming using robust principal component analysis. In Proc. IEEE Intl. Conf. On Image Processing, 2011.
    • (2011) Proc. IEEE Intl. Conf. On Image Processing
    • Tan, W.1    Cheung, G.2    Ma, Y.3
  • 47
    • 78049448383 scopus 로고    scopus 로고
    • An accelerated proximal gradient algorithm for nuclear norm regularized least squares problem
    • K. C. Toh and S. W. Yun. An accelerated proximal gradient algorithm for nuclear norm regularized least squares problem. Pacific Journal of Optimization, 6:615-640, 2010.
    • (2010) Pacific Journal of Optimization , vol.6 , pp. 615-640
    • Toh, K.C.1    Yun, S.W.2
  • 49
    • 77951191949 scopus 로고    scopus 로고
    • Analysis of multi-stage convex relaxation for sparse regularization
    • T. Zhang. Analysis of multi-stage convex relaxation for sparse regularization. Journal of Machine Learning Research, 11:1081-1107, 2010.
    • (2010) Journal of Machine Learning Research , vol.11 , pp. 1081-1107
    • Zhang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.