-
Previous Article
Born to be big: Data, graphs, and their entangled complexity
- BDIA Home
- This Issue
- Next Article
A review on low-rank models in data analysis
1. | Key Lab. of Machine Perception (MOE), School of EECS, Peking University, Beijing, China |
References:
[1] |
A. Adler, M. Elad and Y. Hel-Or, Probabilistic subspace clustering via sparse representations, IEEE Signal Processing Letters, 20 (2013), 63-66.
doi: 10.1109/LSP.2012.2229705. |
[2] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences, 2 (2009), 183-202.
doi: 10.1137/080716542. |
[3] |
J. Cai, E. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2010), 1956-1982.
doi: 10.1137/080738970. |
[4] |
E. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?, Journal of the ACM, 58 (2011), Art. 11, 37 pp.
doi: 10.1145/1970392.1970395. |
[5] |
E. Candès and Y. Plan, Matrix completion with noise, Proceedings of the IEEE, 98 (2010), 925-936. |
[6] |
E. Candès and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational Mathematics, 9 (2009), 717-772.
doi: 10.1007/s10208-009-9045-5. |
[7] |
V. Chandrasekaran, S. Sanghavi, P. Parrilo and A. Willsky, Sparse and low-rank matrix decompositions, Annual Allerton Conference on Communication, Control, and Computing, 2009, 962-967. |
[8] |
C. Chen, B. He, Y. Ye and X. Yuan, The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Mathematical Programming, 155 (2016), 57-79.
doi: 10.1007/s10107-014-0826-5. |
[9] |
Y. Chen, H. Xu, C. Caramanis and S. Sanghavi, Robust matrix completion with corrupted columns, International Conference on Machine Learning, 2011, 873-880. |
[10] |
B. Cheng, G. Liu, J. Wang, Z. Huang and S. Yan, Multi-task low-rank affinity pursuit for image segmentation, International Conference on Computer Vision, 2011, 2439-2446.
doi: 10.1109/ICCV.2011.6126528. |
[11] |
A. Cichocki, R. Zdunek, A. H. Phan and S. Ichi Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation, 1st edition, Wiley, 2009.
doi: 10.1002/9780470747278. |
[12] |
Y. Cui, C.-H. Zheng and J. Yang, Identifying subspace gene clusters from microarray data using low-rank representation, PLoS One, 8 (2013), e59377.
doi: 10.1371/journal.pone.0059377. |
[13] |
P. Drineas, R. Kannan and M. Mahoney, Fast Monte Carlo algorithms for matrices II: Computing a low rank approximation to a matrix, SIAM Journal on Computing, 36 (2006), 158-183.
doi: 10.1137/S0097539704442696. |
[14] |
E. Elhamifar and R. Vidal, Sparse subspace clustering, in IEEE International Conference on Computer Vision and Pattern Recognition, 2009, 2790-2797.
doi: 10.1109/CVPR.2009.5206547. |
[15] |
E. Elhamifar and R. Vidal, Sparse subspace clustering: Algorithm, theory, and applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 2765-2781.
doi: 10.1109/TPAMI.2013.57. |
[16] |
P. Favaro, R. Vidal and A. Ravichandran, A closed form solution to robust subspace estimation and clustering, IEEE Conference on Computer Vision and Pattern Recognition, 2011, 1801-1807.
doi: 10.1109/CVPR.2011.5995365. |
[17] |
J. Feng, Z. Lin, H. Xu and S. Yan, Robust subspace segmentation with block-diagonal prior, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 3818-3825.
doi: 10.1109/CVPR.2014.482. |
[18] |
M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Research Logistics Quarterly, 3 (1956), 95-110.
doi: 10.1002/nav.3800030109. |
[19] |
Y. Fu, J. Gao, D. Tien and Z. Lin, Tensor LRR based subspace clustering, International Joint Conference on Neural Networks, 2014, 1877-1884.
doi: 10.1109/IJCNN.2014.6889472. |
[20] |
A. Ganesh, Z. Lin, J. Wright, L. Wu, M. Chen and Y. Ma, Fast algorithms for recovering a corrupted low-rank matrix, International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2009, 213-216.
doi: 10.1109/CAMSAP.2009.5413299. |
[21] |
H. Gao, J.-F. Cai, Z. Shen and H. Zhao, Robust principal component analysis-based four-dimensional computed tomography, Physics in Medicine and Biology, 56 (2011), 3181-3198.
doi: 10.1088/0031-9155/56/11/002. |
[22] |
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming (web page and software), http://cvxr.com/cvx/, 2009. |
[23] |
S. Gu, L. Zhang, W. Zuo and X. Feng, Weighted nuclear norm minimization with application to image denoising, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 2862-2869.
doi: 10.1109/CVPR.2014.366. |
[24] |
H. Hu, Z. Lin, J. Feng and J. Zhou, Smooth representation clustering, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 3834-3841.
doi: 10.1109/CVPR.2014.484. |
[25] |
Y. Hu, D. Zhang, J. Ye, X. Li and X. He, Fast and accurate matrix completion via truncated nuclear norm regularization, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 2117-2130.
doi: 10.1109/TPAMI.2012.271. |
[26] |
M. Jaggi, Revisiting Frank-Wolfe: Projection-free sparse convex optimization, in International Conference on Machine Learning, 2013, 427-435. |
[27] |
M. Jaggi and M. Sulovský, A simple algorithm for nuclear norm regularized problems, in International Conference on Machine Learning, 2010, 471-478. |
[28] |
I. Jhuo, D. Liu, D. Lee and S. Chang, Robust visual domain adaptation with low-rank reconstruction, IEEE Conference on Computer Vision and Pattern Recognition, 2012, 2168-2175. |
[29] |
H. Ji, C. Liu, Z. Shen and Y. Xu, Robust video denoising using low rank matrix completion, IEEE Conference on Computer Vision and Pattern Recognition, 2010, 1791-1798.
doi: 10.1109/CVPR.2010.5539849. |
[30] |
Y. Jin, Q. Wu and L. Liu, Unsupervised upright orientation of man-made models, Graphical Models, 74 (2012), 99-108.
doi: 10.1016/j.gmod.2012.03.007. |
[31] |
T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Review, 51 (2009), 455-500.
doi: 10.1137/07070111X. |
[32] |
C. Lang, G. Liu, J. Yu and S. Yan, Saliency detection by multitask sparsity pursuit, IEEE Transactions on Image Processing, 21 (2012), 1327-1338.
doi: 10.1109/TIP.2011.2169274. |
[33] |
R. M. Larsen, http://sun.stanford.edu/~rmunk/PROPACK/,, 2004., ().
|
[34] |
D. Lee and H. Seung, Learning the parts of objects by non-negative matrix factorization, Nature, 401 (1999), 788. |
[35] |
X. Liang, X. Ren, Z. Zhang and Y. Ma, Repairing sparse low-rank texture, in European Conference on Computer Vision, 7576 (2012), 482-495.
doi: 10.1007/978-3-642-33715-4_35. |
[36] |
Z. Lin, R. Liu and H. Li, Linearized alternating direction method with parallel splitting and adaptive penality for separable convex programs in machine learning, Machine Learning, 99 (2015), 287-325.
doi: 10.1007/s10994-014-5469-5. |
[37] |
Z. Lin, R. Liu and Z. Su, Linearized alternating direction method with adaptive penalty for low-rank representation, Advances in Neural Information Processing Systems, 2011, 612-620. |
[38] |
G. Liu, Z. Lin, S. Yan, J. Sun and Y. Ma, Robust recovery of subspace structures by low-rank representation, IEEE Transactions Pattern Analysis and Machine Intelligence, 35 (2013), 171-184.
doi: 10.1109/TPAMI.2012.88. |
[39] |
G. Liu, Z. Lin and Y. Yu, Robust subspace segmentation by low-rank representation, in International Conference on Machine Learning, 2010, 663-670. |
[40] |
G. Liu, H. Xu and S. Yan, Exact subspace segmentation and outlier detection by low-rank representation, International Conference on Artificial Intelligence and Statistics, 2012, 703-711. |
[41] |
G. Liu and S. Yan, Latent low-rank representation for subspace segmentation and feature extraction, in IEEE International Conference on Computer Vision, IEEE, 2011, 1615-1622.
doi: 10.1109/ICCV.2011.6126422. |
[42] |
J. Liu, P. Musialski, P. Wonka and J. Ye, Tensor completion for estimating missing values in visual data, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 208-220.
doi: 10.1109/TPAMI.2012.39. |
[43] |
R. Liu, Z. Lin, Z. Su and J. Gao, Linear time principal component pursuit and its extensions using $l_1$ filtering, Neurocomputing, 142 (2014), 529-541. |
[44] |
R. Liu, Z. Lin, F. Torre and Z. Su, Fixed-rank representation for unsupervised visual learning, IEEE Conference on Computer Vision and Pattern Recognition, 2012, 598-605. |
[45] |
C. Lu, J. Feng, Z. Lin and S. Yan, Correlation adaptive subspace segmentation by trace lasso, International Conference on Computer Vision, 2013, 1345-1352.
doi: 10.1109/ICCV.2013.170. |
[46] |
C. Lu, Z. Lin and S. Yan, Smoothed low rank and sparse matrix recovery by iteratively reweighted least squared minimization, IEEE Transactions on Image Processing, 24 (2015), 646-654.
doi: 10.1109/TIP.2014.2380155. |
[47] |
C. Lu, H. Min, Z. Zhao, L. Zhu, D. Huang and S. Yan, Robust and efficient subspace segmentation via least squares regression, European Conference on Computer Vision, 7578 (2012), 347-360.
doi: 10.1007/978-3-642-33786-4_26. |
[48] |
C. Lu, C. Zhu, C. Xu, S. Yan and Z. Lin, Generalized singular value thresholding, AAAI Conference on Artificial Intelligence, 2015, 1805-1811. |
[49] |
X. Lu, Y. Wang and Y. Yuan, Graph-regularized low-rank representation for destriping of hyperspectral images, IEEE Transactions on Geoscience and Remote Sensing, 51 (2013), 4009-4018.
doi: 10.1109/TGRS.2012.2226730. |
[50] |
Y. Ma, S. Soatto, J. Kosecka and S. Sastry, An Invitation to 3-D Vision: From Images to Geometric Models, 1st edition, Springer, 2004.
doi: 10.1007/978-0-387-21779-6. |
[51] |
K. Min, Z. Zhang, J. Wright and Y. Ma, Decomposing background topics from keywords by principal component pursuit, in ACM International Conference on Information and Knowledge Management, 2010, 269-278.
doi: 10.1145/1871437.1871475. |
[52] |
Y. Ming and Q. Ruan, Robust sparse bounding sphere for 3D face recognition, Image and Vision Computing, 30 (2012), 524-534.
doi: 10.1016/j.imavis.2012.05.001. |
[53] |
L. Mukherjee, V. Singh, J. Xu and M. Collins, Analyzing the subspace structure of related images: Concurrent segmentation of image sets, European Conference on Computer Vision, 7575 (2012), 128-142.
doi: 10.1007/978-3-642-33765-9_10. |
[54] |
Y. Nesterov, A method of solving a convex programming problem with convergence rate $O(1/k^2)$, (Russian) Dokl. Akad. Nauk SSSR, 269 (1983), 543-547. |
[55] |
Y. Panagakis and C. Kotropoulos, Automatic music tagging by low-rank representation, International Conference on Acoustics, Speech, and Signal Processing, 2012, 497-500.
doi: 10.1109/ICASSP.2012.6287925. |
[56] |
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 Transactions on Pattern Analysis and Machine Intelligence, 34 (2012), 2233-2246. |
[57] |
J. Qian, J. Yang, F. Zhang and Z. Lin, Robust low-rank regularized regression for face recognition with occlusion, The Workshop of IEEE Conference on Computer Vision and Pattern Recognition, 2014, 21-26.
doi: 10.1109/CVPRW.2014.9. |
[58] |
X. Ren and Z. Lin, Linearized alternating direction method with adaptive penalty and warm starts for fast solving transform invariant low-rank textures, International Journal of Computer Vision, 104 (2013), 1-14.
doi: 10.1007/s11263-013-0611-6. |
[59] |
A. P. Singh and G. J. Gordon, A unified view of matrix factorization models, in Proceedings of Machine Learning and Knowledge Discovery in Databases, 5212 (2008), 358-373.
doi: 10.1007/978-3-540-87481-2_24. |
[60] |
H. Tan, J. Feng, G. Feng, W. Wang and Y. Zhang, Traffic volume data outlier recovery via tensor model, Mathematical Problems in Engineering, 2013 (2013), 164810.
doi: 10.1155/2013/164810. |
[61] |
M. Tso, Reduced-rank regression and canonical analysis, Journal of the Royal Statistical Society, Series B (Methodological), 43 (1981), 183-189. |
[62] |
R. Vidal, Y. Ma and S. Sastry, Generalized principal component analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (2005), 1945-1959. |
[63] |
R. Vidal, Subspace clustering, IEEE Signal Processing Magazine, 28 (2011), 52-68.
doi: 10.1109/MSP.2010.939739. |
[64] |
J. Wang, V. Saligrama and D. Castanon, Structural similarity and distance in learning, Annual Allerton Conf. Communication, Control and Computing, 2011, 744-751.
doi: 10.1109/Allerton.2011.6120242. |
[65] |
Y.-X. Wang and Y.-J. Zhang, Nonnegative matrix factorization: A comprehensive review, IEEE Transactions on Knowledge and Data Engineering, 25 (2013), 1336-1353.
doi: 10.1109/TKDE.2012.51. |
[66] |
S. Wei and Z. Lin, Analysis and improvement of low rank representation for subspace segmentation,, , ().
|
[67] |
Z. Wen, W. Yin and Y. Zhang, Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm, Mathematical Programming Computation, 4 (2012), 333-361.
doi: 10.1007/s12532-012-0044-1. |
[68] |
J. Wright, A. Ganesh, S. Rao, Y. Peng and Y. Ma, Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization, Advances in Neural Information Processing Systems, 2009, 2080-2088. |
[69] |
L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang and Y. Ma, Robust photometric stereo via low-rank matrix completion and recovery, Asian Conference on Computer Vision, 2010, 703-717.
doi: 10.1007/978-3-642-19318-7_55. |
[70] |
L. Yang, Y. Lin, Z. Lin and H. Zha, Low rank global geometric consistency for partial-duplicate image search, International Conference on Pattern Recognition, 2014, 3939-3944.
doi: 10.1109/ICPR.2014.675. |
[71] |
M. Yin, J. Gao and Z. Lin, Laplacian regularized low-rank representation and its applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, 38 (2016), 504-517.
doi: 10.1109/TPAMI.2015.2462360. |
[72] |
Y. Yu and D. Schuurmans, Rank/norm regularization with closed-form solutions: Application to subspace clustering, Uncertainty in Artificial Intelligence, 2011, 778-785. |
[73] |
H. Zhang, Z. Lin and C. Zhang, A counterexample for the validity of using nuclear norm as a convex surrogate of rank, European Conference on Machine Learning, 8189 (2013), 226-241.
doi: 10.1007/978-3-642-40991-2_15. |
[74] |
H. Zhang, Z. Lin, C. Zhang and E. Chang, Exact recoverability of robust PCA via outlier pursuit with tight recovery bounds, AAAI Conference on Artificial Intelligence, 2015, 3143-3149. |
[75] |
H. Zhang, Z. Lin, C. Zhang and J. Gao, Robust latent low rank representation for subspace clustering, Neurocomputing, 145 (2014), 369-373.
doi: 10.1016/j.neucom.2014.05.022. |
[76] |
H. Zhang, Z. Lin, C. Zhang and J. Gao, Relation among some low rank subspace recovery models, Neural Computation, 27 (2015), 1915-1950.
doi: 10.1162/NECO_a_00762. |
[77] |
T. Zhang, B. Ghanem, S. Liu and N. Ahuja, Low-rank sparse learning for robust visual tracking, European Conference on Computer Vision, 7577 (2012), 470-484.
doi: 10.1007/978-3-642-33783-3_34. |
[78] |
Z. Zhang, A. Ganesh, X. Liang and Y. Ma, TILT: Transform invariant low-rank textures, International Journal of Computer Vision, 99 (2012), 1-24.
doi: 10.1007/s11263-012-0515-x. |
[79] |
Z. Zhang, X. Liang and Y. Ma, Unwrapping low-rank textures on generalized cylindrical surfaces, International Conference on Computer Vision, 2011, 1347-1354.
doi: 10.1109/ICCV.2011.6126388. |
[80] |
Z. Zhang, Y. Matsushita and Y. Ma, Camera calibration with lens distortion from low-rank textures, IEEE Conference on Computer Vision and Pattern Recognition, 2011, 2321-2328.
doi: 10.1109/CVPR.2011.5995548. |
[81] |
Y. Zheng, X. Zhang, S. Yang and L. Jiao, Low-rank representation with local constraint for graph construction, Neurocomputing, 122 (2013), 398-405.
doi: 10.1016/j.neucom.2013.06.013. |
[82] |
X. Zhou, C. Yang, H. Zhao and W. Yu, Low-rank modeling and its applications in image analysis, ACM Computing Surveys, 47 (2014), p36.
doi: 10.1145/2674559. |
[83] |
G. Zhu, S. Yan and Y. Ma, Image tag refinement towards low-rank, content-tag prior and error sparsity, in International conference on Multimedia, 2010, 461-470.
doi: 10.1145/1873951.1874028. |
[84] |
L. Zhuang, H. Gao, Z. Lin, Y. Ma, X. Zhang and N. Yu, Non-negative low rank and sparse graph for semi-supervised learning, IEEE International Conference on Computer Vision and Pattern Recognition, 2012, 2328-2335. |
[85] |
W. Zuo and Z. Lin, A generalized accelerated proximal gradient approach for total-variation-based image restoration, IEEE Transactions on Image Processing, 20 (2011), 2748-2759.
doi: 10.1109/TIP.2011.2131665. |
show all references
References:
[1] |
A. Adler, M. Elad and Y. Hel-Or, Probabilistic subspace clustering via sparse representations, IEEE Signal Processing Letters, 20 (2013), 63-66.
doi: 10.1109/LSP.2012.2229705. |
[2] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences, 2 (2009), 183-202.
doi: 10.1137/080716542. |
[3] |
J. Cai, E. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2010), 1956-1982.
doi: 10.1137/080738970. |
[4] |
E. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?, Journal of the ACM, 58 (2011), Art. 11, 37 pp.
doi: 10.1145/1970392.1970395. |
[5] |
E. Candès and Y. Plan, Matrix completion with noise, Proceedings of the IEEE, 98 (2010), 925-936. |
[6] |
E. Candès and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational Mathematics, 9 (2009), 717-772.
doi: 10.1007/s10208-009-9045-5. |
[7] |
V. Chandrasekaran, S. Sanghavi, P. Parrilo and A. Willsky, Sparse and low-rank matrix decompositions, Annual Allerton Conference on Communication, Control, and Computing, 2009, 962-967. |
[8] |
C. Chen, B. He, Y. Ye and X. Yuan, The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Mathematical Programming, 155 (2016), 57-79.
doi: 10.1007/s10107-014-0826-5. |
[9] |
Y. Chen, H. Xu, C. Caramanis and S. Sanghavi, Robust matrix completion with corrupted columns, International Conference on Machine Learning, 2011, 873-880. |
[10] |
B. Cheng, G. Liu, J. Wang, Z. Huang and S. Yan, Multi-task low-rank affinity pursuit for image segmentation, International Conference on Computer Vision, 2011, 2439-2446.
doi: 10.1109/ICCV.2011.6126528. |
[11] |
A. Cichocki, R. Zdunek, A. H. Phan and S. Ichi Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation, 1st edition, Wiley, 2009.
doi: 10.1002/9780470747278. |
[12] |
Y. Cui, C.-H. Zheng and J. Yang, Identifying subspace gene clusters from microarray data using low-rank representation, PLoS One, 8 (2013), e59377.
doi: 10.1371/journal.pone.0059377. |
[13] |
P. Drineas, R. Kannan and M. Mahoney, Fast Monte Carlo algorithms for matrices II: Computing a low rank approximation to a matrix, SIAM Journal on Computing, 36 (2006), 158-183.
doi: 10.1137/S0097539704442696. |
[14] |
E. Elhamifar and R. Vidal, Sparse subspace clustering, in IEEE International Conference on Computer Vision and Pattern Recognition, 2009, 2790-2797.
doi: 10.1109/CVPR.2009.5206547. |
[15] |
E. Elhamifar and R. Vidal, Sparse subspace clustering: Algorithm, theory, and applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 2765-2781.
doi: 10.1109/TPAMI.2013.57. |
[16] |
P. Favaro, R. Vidal and A. Ravichandran, A closed form solution to robust subspace estimation and clustering, IEEE Conference on Computer Vision and Pattern Recognition, 2011, 1801-1807.
doi: 10.1109/CVPR.2011.5995365. |
[17] |
J. Feng, Z. Lin, H. Xu and S. Yan, Robust subspace segmentation with block-diagonal prior, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 3818-3825.
doi: 10.1109/CVPR.2014.482. |
[18] |
M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Research Logistics Quarterly, 3 (1956), 95-110.
doi: 10.1002/nav.3800030109. |
[19] |
Y. Fu, J. Gao, D. Tien and Z. Lin, Tensor LRR based subspace clustering, International Joint Conference on Neural Networks, 2014, 1877-1884.
doi: 10.1109/IJCNN.2014.6889472. |
[20] |
A. Ganesh, Z. Lin, J. Wright, L. Wu, M. Chen and Y. Ma, Fast algorithms for recovering a corrupted low-rank matrix, International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2009, 213-216.
doi: 10.1109/CAMSAP.2009.5413299. |
[21] |
H. Gao, J.-F. Cai, Z. Shen and H. Zhao, Robust principal component analysis-based four-dimensional computed tomography, Physics in Medicine and Biology, 56 (2011), 3181-3198.
doi: 10.1088/0031-9155/56/11/002. |
[22] |
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming (web page and software), http://cvxr.com/cvx/, 2009. |
[23] |
S. Gu, L. Zhang, W. Zuo and X. Feng, Weighted nuclear norm minimization with application to image denoising, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 2862-2869.
doi: 10.1109/CVPR.2014.366. |
[24] |
H. Hu, Z. Lin, J. Feng and J. Zhou, Smooth representation clustering, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 3834-3841.
doi: 10.1109/CVPR.2014.484. |
[25] |
Y. Hu, D. Zhang, J. Ye, X. Li and X. He, Fast and accurate matrix completion via truncated nuclear norm regularization, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 2117-2130.
doi: 10.1109/TPAMI.2012.271. |
[26] |
M. Jaggi, Revisiting Frank-Wolfe: Projection-free sparse convex optimization, in International Conference on Machine Learning, 2013, 427-435. |
[27] |
M. Jaggi and M. Sulovský, A simple algorithm for nuclear norm regularized problems, in International Conference on Machine Learning, 2010, 471-478. |
[28] |
I. Jhuo, D. Liu, D. Lee and S. Chang, Robust visual domain adaptation with low-rank reconstruction, IEEE Conference on Computer Vision and Pattern Recognition, 2012, 2168-2175. |
[29] |
H. Ji, C. Liu, Z. Shen and Y. Xu, Robust video denoising using low rank matrix completion, IEEE Conference on Computer Vision and Pattern Recognition, 2010, 1791-1798.
doi: 10.1109/CVPR.2010.5539849. |
[30] |
Y. Jin, Q. Wu and L. Liu, Unsupervised upright orientation of man-made models, Graphical Models, 74 (2012), 99-108.
doi: 10.1016/j.gmod.2012.03.007. |
[31] |
T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Review, 51 (2009), 455-500.
doi: 10.1137/07070111X. |
[32] |
C. Lang, G. Liu, J. Yu and S. Yan, Saliency detection by multitask sparsity pursuit, IEEE Transactions on Image Processing, 21 (2012), 1327-1338.
doi: 10.1109/TIP.2011.2169274. |
[33] |
R. M. Larsen, http://sun.stanford.edu/~rmunk/PROPACK/,, 2004., ().
|
[34] |
D. Lee and H. Seung, Learning the parts of objects by non-negative matrix factorization, Nature, 401 (1999), 788. |
[35] |
X. Liang, X. Ren, Z. Zhang and Y. Ma, Repairing sparse low-rank texture, in European Conference on Computer Vision, 7576 (2012), 482-495.
doi: 10.1007/978-3-642-33715-4_35. |
[36] |
Z. Lin, R. Liu and H. Li, Linearized alternating direction method with parallel splitting and adaptive penality for separable convex programs in machine learning, Machine Learning, 99 (2015), 287-325.
doi: 10.1007/s10994-014-5469-5. |
[37] |
Z. Lin, R. Liu and Z. Su, Linearized alternating direction method with adaptive penalty for low-rank representation, Advances in Neural Information Processing Systems, 2011, 612-620. |
[38] |
G. Liu, Z. Lin, S. Yan, J. Sun and Y. Ma, Robust recovery of subspace structures by low-rank representation, IEEE Transactions Pattern Analysis and Machine Intelligence, 35 (2013), 171-184.
doi: 10.1109/TPAMI.2012.88. |
[39] |
G. Liu, Z. Lin and Y. Yu, Robust subspace segmentation by low-rank representation, in International Conference on Machine Learning, 2010, 663-670. |
[40] |
G. Liu, H. Xu and S. Yan, Exact subspace segmentation and outlier detection by low-rank representation, International Conference on Artificial Intelligence and Statistics, 2012, 703-711. |
[41] |
G. Liu and S. Yan, Latent low-rank representation for subspace segmentation and feature extraction, in IEEE International Conference on Computer Vision, IEEE, 2011, 1615-1622.
doi: 10.1109/ICCV.2011.6126422. |
[42] |
J. Liu, P. Musialski, P. Wonka and J. Ye, Tensor completion for estimating missing values in visual data, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 208-220.
doi: 10.1109/TPAMI.2012.39. |
[43] |
R. Liu, Z. Lin, Z. Su and J. Gao, Linear time principal component pursuit and its extensions using $l_1$ filtering, Neurocomputing, 142 (2014), 529-541. |
[44] |
R. Liu, Z. Lin, F. Torre and Z. Su, Fixed-rank representation for unsupervised visual learning, IEEE Conference on Computer Vision and Pattern Recognition, 2012, 598-605. |
[45] |
C. Lu, J. Feng, Z. Lin and S. Yan, Correlation adaptive subspace segmentation by trace lasso, International Conference on Computer Vision, 2013, 1345-1352.
doi: 10.1109/ICCV.2013.170. |
[46] |
C. Lu, Z. Lin and S. Yan, Smoothed low rank and sparse matrix recovery by iteratively reweighted least squared minimization, IEEE Transactions on Image Processing, 24 (2015), 646-654.
doi: 10.1109/TIP.2014.2380155. |
[47] |
C. Lu, H. Min, Z. Zhao, L. Zhu, D. Huang and S. Yan, Robust and efficient subspace segmentation via least squares regression, European Conference on Computer Vision, 7578 (2012), 347-360.
doi: 10.1007/978-3-642-33786-4_26. |
[48] |
C. Lu, C. Zhu, C. Xu, S. Yan and Z. Lin, Generalized singular value thresholding, AAAI Conference on Artificial Intelligence, 2015, 1805-1811. |
[49] |
X. Lu, Y. Wang and Y. Yuan, Graph-regularized low-rank representation for destriping of hyperspectral images, IEEE Transactions on Geoscience and Remote Sensing, 51 (2013), 4009-4018.
doi: 10.1109/TGRS.2012.2226730. |
[50] |
Y. Ma, S. Soatto, J. Kosecka and S. Sastry, An Invitation to 3-D Vision: From Images to Geometric Models, 1st edition, Springer, 2004.
doi: 10.1007/978-0-387-21779-6. |
[51] |
K. Min, Z. Zhang, J. Wright and Y. Ma, Decomposing background topics from keywords by principal component pursuit, in ACM International Conference on Information and Knowledge Management, 2010, 269-278.
doi: 10.1145/1871437.1871475. |
[52] |
Y. Ming and Q. Ruan, Robust sparse bounding sphere for 3D face recognition, Image and Vision Computing, 30 (2012), 524-534.
doi: 10.1016/j.imavis.2012.05.001. |
[53] |
L. Mukherjee, V. Singh, J. Xu and M. Collins, Analyzing the subspace structure of related images: Concurrent segmentation of image sets, European Conference on Computer Vision, 7575 (2012), 128-142.
doi: 10.1007/978-3-642-33765-9_10. |
[54] |
Y. Nesterov, A method of solving a convex programming problem with convergence rate $O(1/k^2)$, (Russian) Dokl. Akad. Nauk SSSR, 269 (1983), 543-547. |
[55] |
Y. Panagakis and C. Kotropoulos, Automatic music tagging by low-rank representation, International Conference on Acoustics, Speech, and Signal Processing, 2012, 497-500.
doi: 10.1109/ICASSP.2012.6287925. |
[56] |
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 Transactions on Pattern Analysis and Machine Intelligence, 34 (2012), 2233-2246. |
[57] |
J. Qian, J. Yang, F. Zhang and Z. Lin, Robust low-rank regularized regression for face recognition with occlusion, The Workshop of IEEE Conference on Computer Vision and Pattern Recognition, 2014, 21-26.
doi: 10.1109/CVPRW.2014.9. |
[58] |
X. Ren and Z. Lin, Linearized alternating direction method with adaptive penalty and warm starts for fast solving transform invariant low-rank textures, International Journal of Computer Vision, 104 (2013), 1-14.
doi: 10.1007/s11263-013-0611-6. |
[59] |
A. P. Singh and G. J. Gordon, A unified view of matrix factorization models, in Proceedings of Machine Learning and Knowledge Discovery in Databases, 5212 (2008), 358-373.
doi: 10.1007/978-3-540-87481-2_24. |
[60] |
H. Tan, J. Feng, G. Feng, W. Wang and Y. Zhang, Traffic volume data outlier recovery via tensor model, Mathematical Problems in Engineering, 2013 (2013), 164810.
doi: 10.1155/2013/164810. |
[61] |
M. Tso, Reduced-rank regression and canonical analysis, Journal of the Royal Statistical Society, Series B (Methodological), 43 (1981), 183-189. |
[62] |
R. Vidal, Y. Ma and S. Sastry, Generalized principal component analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27 (2005), 1945-1959. |
[63] |
R. Vidal, Subspace clustering, IEEE Signal Processing Magazine, 28 (2011), 52-68.
doi: 10.1109/MSP.2010.939739. |
[64] |
J. Wang, V. Saligrama and D. Castanon, Structural similarity and distance in learning, Annual Allerton Conf. Communication, Control and Computing, 2011, 744-751.
doi: 10.1109/Allerton.2011.6120242. |
[65] |
Y.-X. Wang and Y.-J. Zhang, Nonnegative matrix factorization: A comprehensive review, IEEE Transactions on Knowledge and Data Engineering, 25 (2013), 1336-1353.
doi: 10.1109/TKDE.2012.51. |
[66] |
S. Wei and Z. Lin, Analysis and improvement of low rank representation for subspace segmentation,, , ().
|
[67] |
Z. Wen, W. Yin and Y. Zhang, Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm, Mathematical Programming Computation, 4 (2012), 333-361.
doi: 10.1007/s12532-012-0044-1. |
[68] |
J. Wright, A. Ganesh, S. Rao, Y. Peng and Y. Ma, Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization, Advances in Neural Information Processing Systems, 2009, 2080-2088. |
[69] |
L. Wu, A. Ganesh, B. Shi, Y. Matsushita, Y. Wang and Y. Ma, Robust photometric stereo via low-rank matrix completion and recovery, Asian Conference on Computer Vision, 2010, 703-717.
doi: 10.1007/978-3-642-19318-7_55. |
[70] |
L. Yang, Y. Lin, Z. Lin and H. Zha, Low rank global geometric consistency for partial-duplicate image search, International Conference on Pattern Recognition, 2014, 3939-3944.
doi: 10.1109/ICPR.2014.675. |
[71] |
M. Yin, J. Gao and Z. Lin, Laplacian regularized low-rank representation and its applications, IEEE Transactions on Pattern Analysis and Machine Intelligence, 38 (2016), 504-517.
doi: 10.1109/TPAMI.2015.2462360. |
[72] |
Y. Yu and D. Schuurmans, Rank/norm regularization with closed-form solutions: Application to subspace clustering, Uncertainty in Artificial Intelligence, 2011, 778-785. |
[73] |
H. Zhang, Z. Lin and C. Zhang, A counterexample for the validity of using nuclear norm as a convex surrogate of rank, European Conference on Machine Learning, 8189 (2013), 226-241.
doi: 10.1007/978-3-642-40991-2_15. |
[74] |
H. Zhang, Z. Lin, C. Zhang and E. Chang, Exact recoverability of robust PCA via outlier pursuit with tight recovery bounds, AAAI Conference on Artificial Intelligence, 2015, 3143-3149. |
[75] |
H. Zhang, Z. Lin, C. Zhang and J. Gao, Robust latent low rank representation for subspace clustering, Neurocomputing, 145 (2014), 369-373.
doi: 10.1016/j.neucom.2014.05.022. |
[76] |
H. Zhang, Z. Lin, C. Zhang and J. Gao, Relation among some low rank subspace recovery models, Neural Computation, 27 (2015), 1915-1950.
doi: 10.1162/NECO_a_00762. |
[77] |
T. Zhang, B. Ghanem, S. Liu and N. Ahuja, Low-rank sparse learning for robust visual tracking, European Conference on Computer Vision, 7577 (2012), 470-484.
doi: 10.1007/978-3-642-33783-3_34. |
[78] |
Z. Zhang, A. Ganesh, X. Liang and Y. Ma, TILT: Transform invariant low-rank textures, International Journal of Computer Vision, 99 (2012), 1-24.
doi: 10.1007/s11263-012-0515-x. |
[79] |
Z. Zhang, X. Liang and Y. Ma, Unwrapping low-rank textures on generalized cylindrical surfaces, International Conference on Computer Vision, 2011, 1347-1354.
doi: 10.1109/ICCV.2011.6126388. |
[80] |
Z. Zhang, Y. Matsushita and Y. Ma, Camera calibration with lens distortion from low-rank textures, IEEE Conference on Computer Vision and Pattern Recognition, 2011, 2321-2328.
doi: 10.1109/CVPR.2011.5995548. |
[81] |
Y. Zheng, X. Zhang, S. Yang and L. Jiao, Low-rank representation with local constraint for graph construction, Neurocomputing, 122 (2013), 398-405.
doi: 10.1016/j.neucom.2013.06.013. |
[82] |
X. Zhou, C. Yang, H. Zhao and W. Yu, Low-rank modeling and its applications in image analysis, ACM Computing Surveys, 47 (2014), p36.
doi: 10.1145/2674559. |
[83] |
G. Zhu, S. Yan and Y. Ma, Image tag refinement towards low-rank, content-tag prior and error sparsity, in International conference on Multimedia, 2010, 461-470.
doi: 10.1145/1873951.1874028. |
[84] |
L. Zhuang, H. Gao, Z. Lin, Y. Ma, X. Zhang and N. Yu, Non-negative low rank and sparse graph for semi-supervised learning, IEEE International Conference on Computer Vision and Pattern Recognition, 2012, 2328-2335. |
[85] |
W. Zuo and Z. Lin, A generalized accelerated proximal gradient approach for total-variation-based image restoration, IEEE Transactions on Image Processing, 20 (2011), 2748-2759.
doi: 10.1109/TIP.2011.2131665. |
[1] |
Yun Cai, Song Li. Convergence and stability of iteratively reweighted least squares for low-rank matrix recovery. Inverse Problems and Imaging, 2017, 11 (4) : 643-661. doi: 10.3934/ipi.2017030 |
[2] |
Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006 |
[3] |
Yangyang Xu, Ruru Hao, Wotao Yin, Zhixun Su. Parallel matrix factorization for low-rank tensor completion. Inverse Problems and Imaging, 2015, 9 (2) : 601-624. doi: 10.3934/ipi.2015.9.601 |
[4] |
Simon Foucart, Richard G. Lynch. Recovering low-rank matrices from binary measurements. Inverse Problems and Imaging, 2019, 13 (4) : 703-720. doi: 10.3934/ipi.2019032 |
[5] |
Simon Arridge, Pascal Fernsel, Andreas Hauptmann. Joint reconstruction and low-rank decomposition for dynamic inverse problems. Inverse Problems and Imaging, 2022, 16 (3) : 483-523. doi: 10.3934/ipi.2021059 |
[6] |
Ke Wei, Jian-Feng Cai, Tony F. Chan, Shingyu Leung. Guarantees of riemannian optimization for low rank matrix completion. Inverse Problems and Imaging, 2020, 14 (2) : 233-265. doi: 10.3934/ipi.2020011 |
[7] |
Haixia Liu, Jian-Feng Cai, Yang Wang. Subspace clustering by (k,k)-sparse matrix factorization. Inverse Problems and Imaging, 2017, 11 (3) : 539-551. doi: 10.3934/ipi.2017025 |
[8] |
Dan Zhu, Rosemary A. Renaut, Hongwei Li, Tianyou Liu. Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory. Inverse Problems and Imaging, 2021, 15 (1) : 159-183. doi: 10.3934/ipi.2020076 |
[9] |
Wei Wan, Weihong Guo, Jun Liu, Haiyang Huang. Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank. Inverse Problems and Imaging, 2020, 14 (2) : 339-361. doi: 10.3934/ipi.2020015 |
[10] |
Guojun Gan, Kun Chen. A soft subspace clustering algorithm with log-transformed distances. Big Data & Information Analytics, 2016, 1 (1) : 93-109. doi: 10.3934/bdia.2016.1.93 |
[11] |
Hua Huang, Weiwei Wang, Chengwu Lu, Xiangchu Feng, Ruiqiang He. Side-information-induced reweighted sparse subspace clustering. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1235-1252. doi: 10.3934/jimo.2020019 |
[12] |
Mingchao Zhao, You-Wei Wen, Michael Ng, Hongwei Li. A nonlocal low rank model for poisson noise removal. Inverse Problems and Imaging, 2021, 15 (3) : 519-537. doi: 10.3934/ipi.2021003 |
[13] |
Xin Zhang, Jie Wen, Qin Ni. Subspace trust-region algorithm with conic model for unconstrained optimization. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 223-234. doi: 10.3934/naco.2013.3.223 |
[14] |
Antonio Cossidente, Sascha Kurz, Giuseppe Marino, Francesco Pavese. Combining subspace codes. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021007 |
[15] |
Michael Kiermaier, Reinhard Laue. Derived and residual subspace designs. Advances in Mathematics of Communications, 2015, 9 (1) : 105-115. doi: 10.3934/amc.2015.9.105 |
[16] |
Heide Gluesing-Luerssen, Carolyn Troha. Construction of subspace codes through linkage. Advances in Mathematics of Communications, 2016, 10 (3) : 525-540. doi: 10.3934/amc.2016023 |
[17] |
Ernst M. Gabidulin, Pierre Loidreau. Properties of subspace subcodes of Gabidulin codes. Advances in Mathematics of Communications, 2008, 2 (2) : 147-157. doi: 10.3934/amc.2008.2.147 |
[18] |
Afaf Bouharguane, Pascal Azerad, Frédéric Bouchette, Fabien Marche, Bijan Mohammadi. Low complexity shape optimization & a posteriori high fidelity validation. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 759-772. doi: 10.3934/dcdsb.2010.13.759 |
[19] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[20] |
Changming Song, Yun Wang. Nonlocal latent low rank sparse representation for single image super resolution via self-similarity learning. Inverse Problems and Imaging, 2021, 15 (6) : 1347-1362. doi: 10.3934/ipi.2021017 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]