Citation: Zhouchen Lin. A Review on Low-Rank Models in Data Analysis[J]. Big Data and Information Analytics, 2016, 1(2): 139-161. doi: 10.3934/bdia.2016001
[1] | [ A. Adler, M. Elad and Y. Hel-Or, Probabilistic subspace clustering via sparse representations, IEEE Signal Processing Letters, 20(2013), 63-66. |
[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. |
[3] | [ J. Cai, E. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20(2010), 1956-1982. |
[4] | [ E. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?, Journal of the ACM, 58(2011), Art. 11, 37 pp. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[14] | [ E. Elhamifar and R. Vidal, Sparse subspace clustering, in IEEE International Conference on Computer Vision and Pattern Recognition, 2009, 2790-2797. |
[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. |
[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. |
[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. |
[18] | [ M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Research Logistics Quarterly, 3(1956), 95-110. |
[19] | [ Y. Fu, J. Gao, D. Tien and Z. Lin, Tensor LRR based subspace clustering, International Joint Conference on Neural Networks, 2014, 1877-1884. |
[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 MultiSensor Adaptive Processing, 2009, 213-216. |
[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. |
[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. |
[24] | [ H. Hu, Z. Lin, J. Feng and J. Zhou, Smooth representation clustering, IEEE Conference on Computer Vision and Pattern Recognition, 2014, 3834-3841. |
[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. |
[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. |
[30] | [ Y. Jin, Q. Wu and L. Liu, Unsupervised upright orientation of man-made models, Graphical Models, 74(2012), 99-108. |
[31] | [ T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Review, 51(2009), 455-500. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[43] | [ R. Liu, Z. Lin, Z. Su and J. Gao, Linear time principal component pursuit and its extensions using l1 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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[52] | [ Y. Ming and Q. Ruan, Robust sparse bounding sphere for 3D face recognition, Image and Vision Computing, 30(2012), 524-534. |
[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. |
[54] | [ Y. Nesterov, A method of solving a convex programming problem with convergence rate O(1/k2), (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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[64] | [ J. Wang, V. Saligrama and D. Castanon, Structural similarity and distance in learning, Annual Allerton Conf. Communication, Control and Computing, 2011, 744-751. |
[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. |
[66] | [ S. Wei and Z. Lin, Analysis and improvement of low rank representation for subspace segmentation, arXiv:1107.1561. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[76] | [ H. Zhang, Z. Lin, C. Zhang and J. Gao, Relation among some low rank subspace recovery models, Neural Computation, 27(2015), 1915-1950. |
[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. |
[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. |
[79] | [ Z. Zhang, X. Liang and Y. Ma, Unwrapping low-rank textures on generalized cylindrical surfaces, International Conference on Computer Vision, 2011, 1347-1354. |
[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. |
[81] | [ Y. Zheng, X. Zhang, S. Yang and L. Jiao, Low-rank representation with local constraint for graph construction, Neurocomputing, 122(2013), 398-405. |
[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. |
[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. |
[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. |