publication . Preprint . 2018

A Comprehensive Survey for Low Rank Regularization

Hu, Zhanxuan; Nie, Feiping; Tian, Lai; Wang, Rong; Li, Xuelong;
Open Access English
  • Published: 14 Aug 2018
Abstract
Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer version. Over the last decade, much progress has been made in theories and practical applications. Nevertheless, the intersection between them is very slight. In order to construct a bridge between practical applications and theoretical research, in this paper we provide a comprehensive survey for low rank regularization. We first review several traditional machine learning models using low rank regularization, and then show their ...
Subjects
free text keywords: Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning
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104 references, page 1 of 7

[1] [2] [3] [4] M. Fazel, “Matrix rank minimization with applications,” Ph.D. dissertation, PhD thesis, Stanford UniverE. J. Cande`s, X. Li, Y. Ma, and J. Wright, “Robust principal component analysis?” Journal of the ACM [10] G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, of subspaces,” in 2014 IEEE Conference on Computer “Robust recovery of subspace structures by low-rank Vision and Pattern Recognition, CVPR 2014, Columbus, representation,” IEEE Trans. Pattern Anal. Mach. Intell., OH, USA, June 23-28, 2014, pp. 1542-1549.

vol. 35, no. 1, pp. 171-184, 2013. [25] Y. Dai, H. Li, and M. He, “A simple prior-free method [11] C. Zhang, Q. Hu, H. Fu, P. Zhu, and X. Cao, “Latent for non-rigid structure-from-motion factorization,” in multi-view subspace clustering,” in 2017 IEEE Confer- 2012 IEEE Conference on Computer Vision and Pattern ence on Computer Vision and Pattern Recognition, CVPR Recognition, Providence, RI, USA, June 16-21, 2012, pp.

2017, Honolulu, HI, USA, July 21-26, 2017, 2017, pp. 2018-2025.

4333-4341. [26] H. Peng, B. Li, H. Ling, W. Hu, W. Xiong, and S. J.

[12] M. Yin, J. Gao, and Z. Lin, “Laplacian regularized low- Maybank, “Salient object detection via structured rank representation and its applications,” IEEE Trans. matrix decomposition,” IEEE Trans. Pattern Anal. Mach.

Pattern Anal. Mach. Intell., vol. 38, no. 3, pp. 504-517, Intell., vol. 39, no. 4, pp. 818-832, 2017.

2016. [27] X. Shen and Y. Wu, “A unified approach to salient [13] Z. Zhang, Y. Xu, L. Shao, and J. Yang, “Discrimina- object detection via low rank matrix recovery,” in tive block-diagonal representation learning for image 2012 IEEE Conference on Computer Vision and Pattern recognition,” IEEE Trans. Neural Netw. Learning Syst., Recognition, Providence, RI, USA, June 16-21, 2012, 2012, vol. 29, no. 7, pp. 3111-3125, 2018. pp. 853-860.

[14] C. Peng, Z. Kang, H. Li, and Q. Cheng, “Subspace [28] W. Zou, K. Kpalma, Z. Liu, and J. Ronsin, “Segmenclustering using log-determinant rank approximation,” tation driven low-rank matrix recovery for saliency in Proceedings of the 21th ACM SIGKDD International detection,” in British Machine Vision Conference, BMVC Conference on Knowledge Discovery and Data Mining. 2013, Bristol, UK, September 9-13, 2013, 2013.

ACM, 2015, pp. 925-934. [29] Z. Gao, L.-F. Cheong, and Y.-X. Wang, “Block-sparse [15] L. Han and Y. Zhang, “Multi-stage multi-task learning rpca for salient motion detection,” IEEE transactions on with reduced rank,” in Proceedings of the Thirtieth AAAI pattern analysis and machine intelligence, vol. 36, no. 10, Conference on Artificial Intelligence, February 12-17, 2016, pp. 1975-1987, 2014.

Phoenix, Arizona, USA., 2016, pp. 1638-1644. [30] Y. Hu, D. Zhang, J. Ye, X. Li, and X. He, “Fast and [16] X. Zhen, M. Yu, X. He, and S. Li, “Multi-target regres- accurate matrix completion via truncated nuclear norm sion via robust low-rank learning,” IEEE Trans. Pattern regularization,” IEEE Trans. Pattern Anal. Mach. Intell., Anal. Mach. Intell., vol. 40, no. 2, pp. 497-504, 2018. vol. 35, no. 9, pp. 2117-2130, 2013.

[17] J. Chen, J. Zhou, and J. Ye, “Integrating low-rank and [31] S. Gu, L. Zhang, W. Zuo, and X. Feng, “Weighted group-sparse structures for robust multi-task learning,” nuclear norm minimization with application to image in Proceedings of the 17th ACM SIGKDD International denoising,” in 2014 IEEE Conference on Computer Vision Conference on Knowledge Discovery and Data Mining, San and Pattern Recognition, CVPR 2014, Columbus, OH, Diego, CA, USA, August 21-24, 2011, 2011, pp. 42-50. USA, June 23-28, 2014, 2014, pp. 2862-2869.

[18] S. Ji and J. Ye, “An accelerated gradient method for [32] S. Gu, Q. Xie, D. Meng, W. Zuo, X. Feng, and L. Zhang, trace norm minimization,” in Proceedings of the 26th “Weighted nuclear norm minimization and its appliAnnual International Conference on Machine Learning, cations to low level vision,” International Journal of ICML 2009, Montreal, Quebec, Canada, June 14-18, 2009, Computer Vision, vol. 121, no. 2, pp. 183-208, 2017.

2009, pp. 457-464. [33] X. Zhong, L. Xu, Y. Li, Z. Liu, and E. Chen, “A [19] Z. Ding and Y. Fu, “Robust multiview data analysis nonconvex relaxation approach for rank minimization through collective low-rank subspace,” IEEE Trans. problems,” in Proceedings of the Twenty-Ninth AAAI Neural Netw. Learning Syst., vol. 29, no. 5, pp. 1986- Conference on Artificial Intelligence, January 25-30, 2015, 1997, 2018. Austin, Texas, USA., pp. 1980-1987.

[20] Y. Sui, Y. Tang, L. Zhang, and G. Wang, “Visual tracking [34] K. Mohan and M. Fazel, “Iterative reweighted algovia subspace learning: A discriminative approach,” rithms for matrix rank minimization.” International Journal of Computer Vision, vol. 126, no. 5, [35] F. Nie, H. Huang, and C. H. Q. Ding, “Low-rank matrix pp. 515-536, 2018. recovery via efficient schatten p-norm minimization,” [21] Y. Sui and L. Zhang, “Robust tracking via locally struc- in Proceedings of the Twenty-Sixth AAAI Conference on tured representation,” International Journal of Computer Artificial Intelligence, July 22-26, 2012, Toronto, Ontario, Vision, vol. 119, no. 2, pp. 110-144, 2016. Canada., 2012.

[22] A. Agudo, M. Pijoan, and F. Moreno-Noguer, “Image [36] F. Shang, J. Cheng, Y. Liu, Z.-Q. Luo, and Z. Lin, collection pop-up: 3d reconstruction and clustering “Bilinear factor matrix norm minimization for robust of rigid and non-rigid categories,” in Proceedings of pca: Algorithms and applications,” IEEE Transactions the IEEE Conference on Computer Vision and Pattern on Pattern Analysis & Machine Intelligence, no. 1, pp. 1-1, Recognition, 2018, pp. 2607-2615. 2017.

104 references, page 1 of 7
Abstract
Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer version. Over the last decade, much progress has been made in theories and practical applications. Nevertheless, the intersection between them is very slight. In order to construct a bridge between practical applications and theoretical research, in this paper we provide a comprehensive survey for low rank regularization. We first review several traditional machine learning models using low rank regularization, and then show their ...
Subjects
free text keywords: Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning
Download from
104 references, page 1 of 7

[1] [2] [3] [4] M. Fazel, “Matrix rank minimization with applications,” Ph.D. dissertation, PhD thesis, Stanford UniverE. J. Cande`s, X. Li, Y. Ma, and J. Wright, “Robust principal component analysis?” Journal of the ACM [10] G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, of subspaces,” in 2014 IEEE Conference on Computer “Robust recovery of subspace structures by low-rank Vision and Pattern Recognition, CVPR 2014, Columbus, representation,” IEEE Trans. Pattern Anal. Mach. Intell., OH, USA, June 23-28, 2014, pp. 1542-1549.

vol. 35, no. 1, pp. 171-184, 2013. [25] Y. Dai, H. Li, and M. He, “A simple prior-free method [11] C. Zhang, Q. Hu, H. Fu, P. Zhu, and X. Cao, “Latent for non-rigid structure-from-motion factorization,” in multi-view subspace clustering,” in 2017 IEEE Confer- 2012 IEEE Conference on Computer Vision and Pattern ence on Computer Vision and Pattern Recognition, CVPR Recognition, Providence, RI, USA, June 16-21, 2012, pp.

2017, Honolulu, HI, USA, July 21-26, 2017, 2017, pp. 2018-2025.

4333-4341. [26] H. Peng, B. Li, H. Ling, W. Hu, W. Xiong, and S. J.

[12] M. Yin, J. Gao, and Z. Lin, “Laplacian regularized low- Maybank, “Salient object detection via structured rank representation and its applications,” IEEE Trans. matrix decomposition,” IEEE Trans. Pattern Anal. Mach.

Pattern Anal. Mach. Intell., vol. 38, no. 3, pp. 504-517, Intell., vol. 39, no. 4, pp. 818-832, 2017.

2016. [27] X. Shen and Y. Wu, “A unified approach to salient [13] Z. Zhang, Y. Xu, L. Shao, and J. Yang, “Discrimina- object detection via low rank matrix recovery,” in tive block-diagonal representation learning for image 2012 IEEE Conference on Computer Vision and Pattern recognition,” IEEE Trans. Neural Netw. Learning Syst., Recognition, Providence, RI, USA, June 16-21, 2012, 2012, vol. 29, no. 7, pp. 3111-3125, 2018. pp. 853-860.

[14] C. Peng, Z. Kang, H. Li, and Q. Cheng, “Subspace [28] W. Zou, K. Kpalma, Z. Liu, and J. Ronsin, “Segmenclustering using log-determinant rank approximation,” tation driven low-rank matrix recovery for saliency in Proceedings of the 21th ACM SIGKDD International detection,” in British Machine Vision Conference, BMVC Conference on Knowledge Discovery and Data Mining. 2013, Bristol, UK, September 9-13, 2013, 2013.

ACM, 2015, pp. 925-934. [29] Z. Gao, L.-F. Cheong, and Y.-X. Wang, “Block-sparse [15] L. Han and Y. Zhang, “Multi-stage multi-task learning rpca for salient motion detection,” IEEE transactions on with reduced rank,” in Proceedings of the Thirtieth AAAI pattern analysis and machine intelligence, vol. 36, no. 10, Conference on Artificial Intelligence, February 12-17, 2016, pp. 1975-1987, 2014.

Phoenix, Arizona, USA., 2016, pp. 1638-1644. [30] Y. Hu, D. Zhang, J. Ye, X. Li, and X. He, “Fast and [16] X. Zhen, M. Yu, X. He, and S. Li, “Multi-target regres- accurate matrix completion via truncated nuclear norm sion via robust low-rank learning,” IEEE Trans. Pattern regularization,” IEEE Trans. Pattern Anal. Mach. Intell., Anal. Mach. Intell., vol. 40, no. 2, pp. 497-504, 2018. vol. 35, no. 9, pp. 2117-2130, 2013.

[17] J. Chen, J. Zhou, and J. Ye, “Integrating low-rank and [31] S. Gu, L. Zhang, W. Zuo, and X. Feng, “Weighted group-sparse structures for robust multi-task learning,” nuclear norm minimization with application to image in Proceedings of the 17th ACM SIGKDD International denoising,” in 2014 IEEE Conference on Computer Vision Conference on Knowledge Discovery and Data Mining, San and Pattern Recognition, CVPR 2014, Columbus, OH, Diego, CA, USA, August 21-24, 2011, 2011, pp. 42-50. USA, June 23-28, 2014, 2014, pp. 2862-2869.

[18] S. Ji and J. Ye, “An accelerated gradient method for [32] S. Gu, Q. Xie, D. Meng, W. Zuo, X. Feng, and L. Zhang, trace norm minimization,” in Proceedings of the 26th “Weighted nuclear norm minimization and its appliAnnual International Conference on Machine Learning, cations to low level vision,” International Journal of ICML 2009, Montreal, Quebec, Canada, June 14-18, 2009, Computer Vision, vol. 121, no. 2, pp. 183-208, 2017.

2009, pp. 457-464. [33] X. Zhong, L. Xu, Y. Li, Z. Liu, and E. Chen, “A [19] Z. Ding and Y. Fu, “Robust multiview data analysis nonconvex relaxation approach for rank minimization through collective low-rank subspace,” IEEE Trans. problems,” in Proceedings of the Twenty-Ninth AAAI Neural Netw. Learning Syst., vol. 29, no. 5, pp. 1986- Conference on Artificial Intelligence, January 25-30, 2015, 1997, 2018. Austin, Texas, USA., pp. 1980-1987.

[20] Y. Sui, Y. Tang, L. Zhang, and G. Wang, “Visual tracking [34] K. Mohan and M. Fazel, “Iterative reweighted algovia subspace learning: A discriminative approach,” rithms for matrix rank minimization.” International Journal of Computer Vision, vol. 126, no. 5, [35] F. Nie, H. Huang, and C. H. Q. Ding, “Low-rank matrix pp. 515-536, 2018. recovery via efficient schatten p-norm minimization,” [21] Y. Sui and L. Zhang, “Robust tracking via locally struc- in Proceedings of the Twenty-Sixth AAAI Conference on tured representation,” International Journal of Computer Artificial Intelligence, July 22-26, 2012, Toronto, Ontario, Vision, vol. 119, no. 2, pp. 110-144, 2016. Canada., 2012.

[22] A. Agudo, M. Pijoan, and F. Moreno-Noguer, “Image [36] F. Shang, J. Cheng, Y. Liu, Z.-Q. Luo, and Z. Lin, collection pop-up: 3d reconstruction and clustering “Bilinear factor matrix norm minimization for robust of rigid and non-rigid categories,” in Proceedings of pca: Algorithms and applications,” IEEE Transactions the IEEE Conference on Computer Vision and Pattern on Pattern Analysis & Machine Intelligence, no. 1, pp. 1-1, Recognition, 2018, pp. 2607-2615. 2017.

104 references, page 1 of 7
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