메뉴 건너뛰기




Volumn 35, Issue 9, 2013, Pages 2117-2130

Fast and accurate matrix completion via truncated nuclear norm regularization

Author keywords

accelerated proximal gradient method; alternating direction method of multipliers; Matrix completion; nuclear norm minimization

Indexed keywords

ACCELERATED PROXIMAL GRADIENT METHODS; ALTERNATING DIRECTION METHOD OF MULTIPLIERS; FASTER CONVERGENCE; LOW-RANK MATRIX APPROXIMATIONS; MATRIX COMPLETION; NUCLEAR NORM MINIMIZATIONS; NUCLEAR NORM REGULARIZATIONS; OPTIMIZATION PROBLEMS;

EID: 84880896128     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2012.271     Document Type: Article
Times cited : (807)

References (48)
  • 1
    • 71049116435 scopus 로고    scopus 로고
    • Exact matrix completion via convex optimization
    • E.J. Candés and B. Recht, "Exact Matrix Completion via Convex Optimization," Foundations on Computational Math., vol. 9, pp. 717-772, 2009.
    • (2009) Foundations on Computational Math , vol.9 , pp. 717-772
    • Candés, E.J.1    Recht, B.2
  • 2
    • 77951528523 scopus 로고    scopus 로고
    • The power of convex relaxation: Near-optimal matrix completion
    • May
    • E.J. Candés and T. Tao, "The Power of Convex Relaxation: Near-Optimal Matrix Completion," IEEE Trans. Information Theory, vol. 56, no. 5, pp. 2053-2080, May 2009.
    • (2009) IEEE Trans. Information Theory , vol.56 , Issue.5 , pp. 2053-2080
    • Candés, E.J.1    Tao, T.2
  • 4
    • 77955994778 scopus 로고    scopus 로고
    • Efficient computation of robust low-rank matrix approximations in the presence of missing data using the l1 norm
    • A. Eriksson and A. van den Hengel, "Efficient Computation of Robust Low-Rank Matrix Approximations in the Presence of Missing Data Using the l1 Norm," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010.
    • (2010) Proc IEEE Conf. Computer Vision and Pattern Recognition
    • Eriksson, A.1    Hengel Den A.Van2
  • 5
    • 84856673250 scopus 로고    scopus 로고
    • Efficient algorithm for low-rank matrix factorization with missing components and performance comparison of latest algorithms
    • T. Okatani, T. Yoshida, and K. Deguchi, "Efficient Algorithm for Low-Rank Matrix Factorization with Missing Components and Performance Comparison of Latest Algorithms," Proc. IEEE Int'l Conf. Computer Vision, 2011.
    • (2011) Proc IEEE Int'l Conf. Computer Vision
    • Okatani, T.1    Yoshida, T.2    Deguchi, K.3
  • 6
    • 0029373923 scopus 로고
    • Principal component analysis with missing data and its application to polyhedral object modeling
    • Sept
    • H.-Y. Shum, K. Ikeuchi, and R. Reddy, "Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 9, pp. 854-867, Sept. 1995.
    • (1995) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.17 , Issue.9 , pp. 854-867
    • Shum, H.-Y.1    Ikeuchi, K.2    Reddy, R.3
  • 7
    • 79251515185 scopus 로고    scopus 로고
    • Trace norm regularization: Reformulation, algorithms, and multi-task learning
    • S.J. Ting Kei Tong, P. Tseng, and J. Ye, "Trace Norm Regularization: Reformulation, Algorithms, and Multi-Task Learning," SIAM J. Optimization, vol. 20, no. 6, pp. 3465-3489, 2010.
    • (2010) SIAM J. Optimization , vol.20 , Issue.6 , pp. 3465-3489
    • Ting Kei Tong, S.J.1    Tseng, P.2    Ye, J.3
  • 9
    • 33749255619 scopus 로고    scopus 로고
    • Spatiotemporal inpainting for recovering texture maps of partially occluded building facades
    • C. Rasmussen and T. Korah, "Spatiotemporal Inpainting for Recovering Texture Maps of Partially Occluded Building Facades," Proc. IEEE Int'l Conf. Image Processing, 2005.
    • (2005) Proc IEEE Int'l Conf. Image Processing
    • Rasmussen, C.1    Korah, T.2
  • 13
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
    • B. Recht, M. Fazel, and P.A. Parrilo, "Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization," SIAM Rev., vol. 52, no. 3, pp. 471-501, 2010.
    • (2010) SIAM Rev , vol.52 , Issue.3 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.A.3
  • 14
    • 79957957723 scopus 로고    scopus 로고
    • Fixed point and bregman iterative methods for matrix rank minimization
    • S. Ma, D. Goldfarb, and L. Chen, "Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization," Math. Programming, vol. 128, nos. 1-2, pp. 321-353, 2011.
    • (2011) Math. Programming , vol.128 , Issue.1-2 , pp. 321-353
    • Ma, S.1    Goldfarb, D.2    Chen, L.3
  • 15
    • 84856009825 scopus 로고    scopus 로고
    • A simpler approach to matrix completion
    • B. Recht, "A Simpler Approach to Matrix Completion," J. Machine Learning Research, vol. 12, pp. 413-3430, 2011.
    • (2011) J. Machine Learning Research , vol.12 , pp. 413-3430
    • Recht, B.1
  • 16
    • 77952741387 scopus 로고    scopus 로고
    • Matrix completion with noise
    • E.J. Candés and Y. Plan, "Matrix Completion with Noise," Proc. IEEE, vol. 98, no. 6, pp. 925-936, 2009.
    • (2009) Proc IEEE , vol.98 , Issue.6 , pp. 925-936
    • Candés, E.J.1    Plan, Y.2
  • 17
    • 77951291046 scopus 로고    scopus 로고
    • A singular value thresholding algorithm for matrix completion
    • J.F. Cai, E.J. Candés, and Z. Shen, "A Singular Value Thresholding Algorithm for Matrix Completion," SIAM J. Optimization, vol. 20, pp. 1956-1982, 2010.
    • (2010) SIAM J. Optimization , vol.20 , pp. 1956-1982
    • Cai, J.F.1    Candés, E.J.2    Shen, Z.3
  • 18
    • 78049448383 scopus 로고    scopus 로고
    • An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems
    • K.-C. Toh and S. Yun, "An Accelerated Proximal Gradient Algorithm for Nuclear Norm Regularized Least Squares Problems," Pacific J. Optimization, pp. 615-640, 2010.
    • (2010) Pacific J. Optimization , pp. 615-640
    • Toh, K.-C.1    Yun, S.2
  • 24
    • 84866665730 scopus 로고    scopus 로고
    • Rasl: Robust alignment by sparse and low-rank decomposition for linearly correlated images
    • Nov
    • Y. Peng, A. Ganesh, J. Wright, W. Xu, and Y. Ma, "RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 34, no. 11, pp. 2233-2246, Nov. 2012.
    • (2012) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.34 , Issue.11 , pp. 2233-2246
    • Peng, Y.1    Ganesh, A.2    Wright, J.3    Xu, W.4    Ma, Y.5
  • 26
    • 0034853839 scopus 로고    scopus 로고
    • A rank minimization heuristic with application to minimum order system approximation
    • M. Fazel, H. Hindi, and S.P. Boyd, "A Rank Minimization Heuristic with Application to Minimum Order System Approximation," Proc. Am. Control Conf., pp. 4734-4739. 2001 (Pubitemid 32837075)
    • (2001) Proceedings of the American Control Conference , vol.6 , pp. 4734-4739
    • Fazel, M.1    Hindi, H.2    Boyd, S.P.3
  • 27
    • 79959203326 scopus 로고    scopus 로고
    • Subspace evolution and transfer (set) for low-rank matrix completion
    • July
    • W. Dai, O. Milenkovic, and E. Kerman, "Subspace Evolution and Transfer (Set) for Low-Rank Matrix Completion," IEEE Trans. Signal Processing, vol. 59, no. 7, pp. 3120-3132, July 2011.
    • (2011) IEEE Trans. Signal Processing , vol.59 , Issue.7 , pp. 3120-3132
    • Dai, W.1    Milenkovic, O.2    Kerman, E.3
  • 35
    • 21644465788 scopus 로고    scopus 로고
    • Local minima and convergence in low-rank semidefinite programming
    • DOI 10.1007/s10107-004-0564-1
    • S. Burer and R.D.C. Monteiro, "Local Minima and Convergence in Low-Rank Semidefinite Programming," Math. Programming, vol. 103, no. 3, pp. 427-444, 2005. (Pubitemid 40925236)
    • (2005) Mathematical Programming , vol.103 , Issue.3 , pp. 427-444
    • Burer, S.1    Monteiro, R.D.C.2
  • 41
    • 80051762104 scopus 로고    scopus 로고
    • Distributed optimization and statistical learning via the alternating direction method of multipliers
    • S. Boyd, N. Parikh, E. Chu, and J. Eckstein, "Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers," Information Systems J., vol. 3, no. 1, pp. 1-122, 2010.
    • (2010) Information Systems J , vol.3 , Issue.1 , pp. 1-122
    • Boyd, S.1    Parikh, N.2    Chu, E.3    Eckstein, J.4
  • 43
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • A. Beck and M. Teboulle, "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems," SIAM J. Imaging Sciences, vol. 2, no. 1, pp. 183-202, 2009.
    • (2009) SIAM J. Imaging Sciences , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 44
    • 34548480020 scopus 로고
    • A method of solving a convex programming problem with convergence rate o(1/sqr(k))
    • Y. Nesterov, "A Method of Solving a Convex Programming Problem with Convergence Rate o(1/sqr(k))," Soviet Math. Doklady, vol. 27, pp. 372-376, 1983.
    • (1983) Soviet Math. Doklady , vol.27 , pp. 372-376
    • Nesterov, Y.1
  • 45
    • 84865692854 scopus 로고    scopus 로고
    • Alternating direction method with gaussian back substitution for separable convex programming
    • B. He, M. Tao, and X. Yuan, "Alternating Direction Method with Gaussian Back Substitution for Separable Convex Programming," SIAM J. Optimization, vol. 22, no. 2, pp. 313-340, 2012.
    • (2012) SIAM J. Optimization , vol.22 , Issue.2 , pp. 313-340
    • He, B.1    Tao, M.2    Yuan, X.3
  • 46
    • 79957510064 scopus 로고    scopus 로고
    • Recovering low-rank and sparse components of matrices from incomplete and noisy observations
    • M. Tao and X. Yuan, "Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations," SIAM J. Optimizaiton, vol. 21, no. 1, pp. 57-81, 2011.
    • (2011) SIAM J. Optimizaiton , vol.21 , Issue.1 , pp. 57-81
    • Tao, M.1    Yuan, X.2
  • 47
    • 0034239566 scopus 로고    scopus 로고
    • Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities
    • B.S. He, H. Yang, and S.L. Wang, "Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities," J. Optimization Theory and Applications, vol. 106, no. 2, pp. 337-356, 2000.
    • (2000) J. Optimization Theory and Applications , vol.106 , Issue.2 , pp. 337-356
    • He, B.S.1    Yang, H.2    Wang, S.L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.