A unified framework for nonconvex nonsmooth sparse and low-rank decomposition by majorization-minimization algorithm
Recovering a low-rank matrix and a sparse matrix from an observed matrix, known as sparse and low-rank decomposition (SLRD), is becoming a hot topic in recent years. The most popular model for SLRD is to use the ℓ1 norm and nuclear norm for the sparse and low-rank approximation. Since this convex mo...
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| Published in: | Journal of the Franklin Institute Vol. 359; no. 16; pp. 9376 - 9400 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.11.2022
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| ISSN: | 0016-0032, 1879-2693 |
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| Abstract | Recovering a low-rank matrix and a sparse matrix from an observed matrix, known as sparse and low-rank decomposition (SLRD), is becoming a hot topic in recent years. The most popular model for SLRD is to use the ℓ1 norm and nuclear norm for the sparse and low-rank approximation. Since this convex model has certain limitations, various nonconvex models have been explored and found to be very promising. In this paper, we introduce a generalized nonconvex nonsmooth model for SLRD which covers a wide range of nonconvex surrogate functions that are continuous, concave and monotonically increasing on [0,∞) to approximate both the ℓ0 norm and the rank function, such as ℓp norm (0<p<1), Logarithm, Geman, SCAD and MCP functions. The choice of the nonconvex surrogates for the sparse and low-rank components can be different. Due to the nonconvexity and extensive options of the surrogates, the optimization problem is untractable. Based on the majorization-minimization (MM) algorithm, we propose a unified framework named MM-ADMM algorithm to solve this problem, which can be applied to all eligible surrogates as long as their supergradients are available. The constrained majorizing problems established under the MM framework can be easily solved by the alternating direction method of multipliers (ADMM). The theoretical convergence properties are investigated and proved, including the convergence of the sequence of objective function values generated by the designed algorithm and a weak convergence result related to the inner ADMM-iterations. Experiments on the synthetic data and real-world applications demonstrate the effectiveness of our designed MM-ADMM algorithm. |
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| AbstractList | Recovering a low-rank matrix and a sparse matrix from an observed matrix, known as sparse and low-rank decomposition (SLRD), is becoming a hot topic in recent years. The most popular model for SLRD is to use the ℓ1 norm and nuclear norm for the sparse and low-rank approximation. Since this convex model has certain limitations, various nonconvex models have been explored and found to be very promising. In this paper, we introduce a generalized nonconvex nonsmooth model for SLRD which covers a wide range of nonconvex surrogate functions that are continuous, concave and monotonically increasing on [0,∞) to approximate both the ℓ0 norm and the rank function, such as ℓp norm (0<p<1), Logarithm, Geman, SCAD and MCP functions. The choice of the nonconvex surrogates for the sparse and low-rank components can be different. Due to the nonconvexity and extensive options of the surrogates, the optimization problem is untractable. Based on the majorization-minimization (MM) algorithm, we propose a unified framework named MM-ADMM algorithm to solve this problem, which can be applied to all eligible surrogates as long as their supergradients are available. The constrained majorizing problems established under the MM framework can be easily solved by the alternating direction method of multipliers (ADMM). The theoretical convergence properties are investigated and proved, including the convergence of the sequence of objective function values generated by the designed algorithm and a weak convergence result related to the inner ADMM-iterations. Experiments on the synthetic data and real-world applications demonstrate the effectiveness of our designed MM-ADMM algorithm. |
| Author | Zheng, Qian-Zhen Xu, Ping-Feng |
| Author_xml | – sequence: 1 givenname: Qian-Zhen surname: Zheng fullname: Zheng, Qian-Zhen organization: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China – sequence: 2 givenname: Ping-Feng orcidid: 0000-0002-4721-9996 surname: Xu fullname: Xu, Ping-Feng email: xupf900@nenu.edu.cn organization: Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun 130024, China |
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| References | Ganesh, Lin, Wright, Wu, Chen, Ma (bib0015) 2009 Yang, Yang, Li (bib0026) 2020; 41 Chen, Zhao, Sun, Li, Feng (bib0040) 2022 Wright, Peng, Ma, Ganesh, Rao (bib0002) 2009 Wang, Wang, Hu, Yan (bib0051) 2015; 48 He, Yang, Wang (bib0054) 2000; 106 Na, Kolar, Koyejo (bib0013) 2021; 108 Abbott (bib0059) 2015 Liu, Zhao, Yao, Qi (bib0005) 2015; 24 Gu, Zhang, Zuo, Feng (bib0037) 2014 Gu, Xie, Meng, Zuo, Feng, Zhang (bib0036) 2017; 121 Zhang, Liu, Tian, Xu, Lu, Ma (bib0007) 2011 Z. Zhou, Y. Ma, Comments on efficient singular value thresholding computation, 2020. Available Lin, Liu, Li (bib0055) 2015; 99 Bouwmans, Zahzah (bib0003) 2014; 122 Netrapalli, UN, Sanghavi, Anandkumar, Jain (bib0045) 2014 Bartle (bib0060) 1976 Chandrasekaran, Sanghavi, Parrilo, Willsky (bib0011) 2009 Wen, Ying, Liu, Trieu-Kien (bib0023) 2019; 67 Chandrasekaran, Parrilo, Willsky (bib0010) 2012; 40 Yang, Pong, Chen (bib0025) 2017; 10 Qian, Cao (bib0034) 2019; 10 Wen, Chu, Liu, Qiu (bib0022) 2018; 6 Zhou, Yang, Zhao, Yu (bib0008) 2015; 47 Sun, Xiang, Ye (bib0021) 2013 Shi, Nie, Lai, Guo (bib0043) 2018; 283 . Dutta, Hanzely, Richtárik (bib0048) 2019 Zhang, Zhou, Wang, Ma (bib0058) 2014 Kang, Peng, Cheng (bib0039) 2015 Li, Dai, Cheng, Xu, Gui (bib0029) 2019; 356 Bouwmans, Aybat, Zahzah (bib0004) 2016 Cai, Cai, We (bib0046) 2019; 20 Zhang, Wang, Zhou, Ma (bib0063) 2019; 43 Yang, Yang, Han (bib0028) 2018; 6 Oh, Tai, Bazin, Kim, Kweon (bib0033) 2016; 38 Dong, Sun, Xu, Liu (bib0009) 2020; 20 Chen, Li (bib0042) 2015; 58 Yuan, Yang (bib0014) 2013; 9 Zhou, Tao (bib0044) 2011 Yang, Yang, Fan, Bao (bib0041) 2022 Li, Liu, Zhao, Cheng, Gui (bib0030) 2020; 357 Fan, Li (bib0061) 2001; 96 Wen, Ying, Liu, Qiu (bib0024) 2020; 30 Candès, Li, Ma, Wright (bib0001) 2011; 58 Xie, Gu, Liu, Zuo, Zhang, Zhang (bib0038) 2016; 25 Wang, Jodoin, Porikli, Konrad, Benezeth, Ishwar (bib0062) 2014 Chandrasekaran, Sanghavi, Parrilo, Willsky (bib0012) 2011; 21 Wang, Liao (bib0056) 2001; 109 Z. Lin, M. Chen, Y. Ma, The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices, (2010). Available Shao, Ge, Gan, Deng, Li (bib0050) 2014; 2014 Yang, Fan, Yang, Yang, Gui (bib0027) 2019; 356 Cao, Chen, Ye, Zhao, Zhou (bib0032) 2017; 85 Zhang, Guo, Zhao, Wang (bib0035) 2016; 21 Dutta, Hanzely, Liang, Richtárik (bib0049) 2020; 68 Hunter, Lange (bib0052) 2004; 58 Luong, Joukovsky, Eldar, Deligiannis (bib0006) 2021 Chartrand (bib0020) 2012; 60 Boyd, Parikh, Chu, Peleato, Eckstein (bib0031) 2011; 3 Lu, Tang, Yan, Lin (bib0017) 2014 Lu, Tang, Yan, Lin (bib0018) 2016; 25 Chen, Dong, Chan (bib0053) 2013; 100 Peng, Ganesh, Wright, Xu, Ma (bib0065) 2012; 34 Lu, Zhu, Xu, Yan, Lin (bib0019) 2015 Zhang, Wang, Gu (bib0047) 2018; vol. 84 Zhang, Wang, Zhou, Ma (bib0064) 2013 Wen (10.1016/j.jfranklin.2022.09.002_bib0022) 2018; 6 Wang (10.1016/j.jfranklin.2022.09.002_bib0056) 2001; 109 Qian (10.1016/j.jfranklin.2022.09.002_bib0034) 2019; 10 Zhang (10.1016/j.jfranklin.2022.09.002_bib0035) 2016; 21 Cai (10.1016/j.jfranklin.2022.09.002_bib0046) 2019; 20 Luong (10.1016/j.jfranklin.2022.09.002_bib0006) 2021 Li (10.1016/j.jfranklin.2022.09.002_bib0030) 2020; 357 Chen (10.1016/j.jfranklin.2022.09.002_bib0040) 2022 Xie (10.1016/j.jfranklin.2022.09.002_bib0038) 2016; 25 Bouwmans (10.1016/j.jfranklin.2022.09.002_bib0003) 2014; 122 Lu (10.1016/j.jfranklin.2022.09.002_bib0018) 2016; 25 Wen (10.1016/j.jfranklin.2022.09.002_bib0023) 2019; 67 Yang (10.1016/j.jfranklin.2022.09.002_bib0025) 2017; 10 Yang (10.1016/j.jfranklin.2022.09.002_bib0026) 2020; 41 Sun (10.1016/j.jfranklin.2022.09.002_bib0021) 2013 Dutta (10.1016/j.jfranklin.2022.09.002_bib0049) 2020; 68 Na (10.1016/j.jfranklin.2022.09.002_bib0013) 2021; 108 Oh (10.1016/j.jfranklin.2022.09.002_bib0033) 2016; 38 Wen (10.1016/j.jfranklin.2022.09.002_bib0024) 2020; 30 Shi (10.1016/j.jfranklin.2022.09.002_bib0043) 2018; 283 Shao (10.1016/j.jfranklin.2022.09.002_bib0050) 2014; 2014 Hunter (10.1016/j.jfranklin.2022.09.002_bib0052) 2004; 58 Cao (10.1016/j.jfranklin.2022.09.002_bib0032) 2017; 85 Zhou (10.1016/j.jfranklin.2022.09.002_bib0044) 2011 He (10.1016/j.jfranklin.2022.09.002_bib0054) 2000; 106 Peng (10.1016/j.jfranklin.2022.09.002_bib0065) 2012; 34 Lu (10.1016/j.jfranklin.2022.09.002_bib0017) 2014 Boyd (10.1016/j.jfranklin.2022.09.002_bib0031) 2011; 3 Fan (10.1016/j.jfranklin.2022.09.002_bib0061) 2001; 96 Yang (10.1016/j.jfranklin.2022.09.002_bib0027) 2019; 356 Zhang (10.1016/j.jfranklin.2022.09.002_bib0047) 2018; vol. 84 Ganesh (10.1016/j.jfranklin.2022.09.002_bib0015) 2009 10.1016/j.jfranklin.2022.09.002_bib0057 Yang (10.1016/j.jfranklin.2022.09.002_bib0041) 2022 10.1016/j.jfranklin.2022.09.002_bib0016 Chen (10.1016/j.jfranklin.2022.09.002_bib0053) 2013; 100 Chandrasekaran (10.1016/j.jfranklin.2022.09.002_bib0012) 2011; 21 Chandrasekaran (10.1016/j.jfranklin.2022.09.002_bib0010) 2012; 40 Liu (10.1016/j.jfranklin.2022.09.002_bib0005) 2015; 24 Zhang (10.1016/j.jfranklin.2022.09.002_bib0058) 2014 Kang (10.1016/j.jfranklin.2022.09.002_bib0039) 2015 Wang (10.1016/j.jfranklin.2022.09.002_bib0062) 2014 Chen (10.1016/j.jfranklin.2022.09.002_bib0042) 2015; 58 Wright (10.1016/j.jfranklin.2022.09.002_bib0002) 2009 Yang (10.1016/j.jfranklin.2022.09.002_bib0028) 2018; 6 Chandrasekaran (10.1016/j.jfranklin.2022.09.002_bib0011) 2009 Zhang (10.1016/j.jfranklin.2022.09.002_bib0064) 2013 Chartrand (10.1016/j.jfranklin.2022.09.002_bib0020) 2012; 60 Dong (10.1016/j.jfranklin.2022.09.002_bib0009) 2020; 20 Yuan (10.1016/j.jfranklin.2022.09.002_bib0014) 2013; 9 Lin (10.1016/j.jfranklin.2022.09.002_bib0055) 2015; 99 Wang (10.1016/j.jfranklin.2022.09.002_bib0051) 2015; 48 Zhang (10.1016/j.jfranklin.2022.09.002_bib0063) 2019; 43 Abbott (10.1016/j.jfranklin.2022.09.002_bib0059) 2015 Gu (10.1016/j.jfranklin.2022.09.002_bib0036) 2017; 121 Candès (10.1016/j.jfranklin.2022.09.002_bib0001) 2011; 58 Li (10.1016/j.jfranklin.2022.09.002_bib0029) 2019; 356 Zhang (10.1016/j.jfranklin.2022.09.002_bib0007) 2011 Zhou (10.1016/j.jfranklin.2022.09.002_bib0008) 2015; 47 Bartle (10.1016/j.jfranklin.2022.09.002_bib0060) 1976 Lu (10.1016/j.jfranklin.2022.09.002_bib0019) 2015 Gu (10.1016/j.jfranklin.2022.09.002_bib0037) 2014 Netrapalli (10.1016/j.jfranklin.2022.09.002_bib0045) 2014 Bouwmans (10.1016/j.jfranklin.2022.09.002_bib0004) 2016 Dutta (10.1016/j.jfranklin.2022.09.002_bib0048) 2019 |
| References_xml | – volume: 67 start-page: 5402 year: 2019 end-page: 5416 ident: bib0023 article-title: Nonconvex regularized robust PCA using the proximal block coordinate descent algorithm publication-title: IEEE Trans. Signal Process. – volume: 108 start-page: 425 year: 2021 end-page: 442 ident: bib0013 article-title: Estimating differential latent variable graphical models with applications to brain connectivity publication-title: Biometrika – volume: 10 start-page: 1341 year: 2019 end-page: 1355 ident: bib0034 article-title: Adaptive algorithms for low-rank and sparse matrix recovery with truncated nuclear norm publication-title: Int. J. Mach. Learn. Cybern. – volume: 3 start-page: 1 year: 2011 end-page: 122 ident: bib0031 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. – volume: 38 start-page: 744 year: 2016 end-page: 758 ident: bib0033 article-title: Partial sum minimization of singular values in robust PCA: algorithm and applications publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 60 start-page: 5810 year: 2012 end-page: 5819 ident: bib0020 article-title: Nonconvex splitting for regularized low-rank + sparse decomposition publication-title: IEEE Trans. Signal Process. – start-page: 311 year: 2013 end-page: 319 ident: bib0021 article-title: Robust principal component analysis via capped norms publication-title: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining – year: 2022 ident: bib0040 article-title: Moving object detection via RPCA framework using non-convex low-rank approximation and total variational regularization publication-title: Signal Image Video Process. – year: 1976 ident: bib0060 article-title: The Elements of Real Analysis – volume: 43 start-page: 238 year: 2019 end-page: 255 ident: bib0063 article-title: Robust low-rank tensor recovery with rectification and alignment publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 6 start-page: 69883 year: 2018 end-page: 69906 ident: bib0022 article-title: A survey on nonconvex regularization-based sparse and low-rank recovery in signal processing, statistics, and machine learning publication-title: IEEE Access, – volume: 47 start-page: 36 year: 2015 ident: bib0008 article-title: Low-rank modeling and its applications in image analysis publication-title: ACM Comput. Surv. – start-page: 1805 year: 2015 end-page: 1811 ident: bib0019 article-title: Generalized singular value thresholding publication-title: Proceedings of the AAAI Conference on Artificial Intelligence – volume: 100 start-page: 901 year: 2013 end-page: 920 ident: bib0053 article-title: Reduced rank regression via adaptive nuclear norm penalization publication-title: Biometrika – volume: 96 start-page: 1348 year: 2001 end-page: 1360 ident: bib0061 article-title: Variable selection via nonconcave penalized likelihood and its oracle properties publication-title: J. Am. Stat. Assoc. – volume: 2014 start-page: 656074 year: 2014 ident: bib0050 article-title: A generalized robust minimization framework for low-rank matrix recovery publication-title: Math. Probl. Eng. – volume: 109 start-page: 415 year: 2001 end-page: 429 ident: bib0056 article-title: Decomposition method with a variable parameter for a class of monotone variational inequality problems publication-title: J. Optim. Theory Appl. – start-page: 1468 year: 2019 end-page: 1476 ident: bib0048 article-title: A nonconvex projection method for robust PCA publication-title: Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19) – volume: 9 start-page: 167 year: 2013 end-page: 180 ident: bib0014 article-title: Sparse and low-rank matrix decomposition via alternating direction method publication-title: Pacific J. Optim. – volume: 283 start-page: 205 year: 2018 end-page: 213 ident: bib0043 article-title: Robust principal component analysis via optimal mean by joint publication-title: Neurocomputing – volume: 48 start-page: 3135 year: 2015 end-page: 3144 ident: bib0051 article-title: Visual data denoising with a unified schatten- publication-title: Pattern Recognit. – year: 2014 ident: bib0045 article-title: Non-convex robust PCA publication-title: Advances in Neural Information Processing Systems – start-page: 2862 year: 2014 end-page: 2869 ident: bib0037 article-title: Weighted nuclear norm minimization with application to image denoising publication-title: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) – volume: 21 start-page: 572 year: 2011 end-page: 596 ident: bib0012 article-title: Rank-sparsity incoherence for matrix decomposition publication-title: SIAM J. Optim. – year: 2009 ident: bib0002 article-title: Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization publication-title: Advances in Neural Information Processing Systems (NIPS) – volume: 40 start-page: 1935 year: 2012 end-page: 1967 ident: bib0010 article-title: Latent variable graphical model selection via convex optimization publication-title: Ann. Stat. – volume: 58 start-page: 30 year: 2004 end-page: 37 ident: bib0052 article-title: A tutorial on MM algorithms publication-title: Am. Stat. – start-page: 33 year: 2011 end-page: 40 ident: bib0044 article-title: GoDec: randomized low-rank & sparse matrix decomposition in noisy case publication-title: Proceedings of the 28th International Conference on Machine Learning, ICML 2011 – volume: 25 start-page: 4842 year: 2016 end-page: 4857 ident: bib0038 article-title: Weighted schatten publication-title: IEEE Trans. Image Process. – volume: 34 start-page: 2233 year: 2012 end-page: 2246 ident: bib0065 article-title: RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 356 start-page: 2353 year: 2019 end-page: 2371 ident: bib0029 article-title: Multiple-prespecified-dictionary sparse representation for compressive sensing image reconstruction with nonconvex regularization publication-title: J. Franklin Inst. – volume: 85 start-page: 10 year: 2017 end-page: 20 ident: bib0032 article-title: Recovering low-rank and sparse matrix based on the truncated nuclear norm publication-title: Neural Netw. – start-page: 1637 year: 2013 end-page: 1645 ident: bib0064 article-title: Simultaneous rectification and alignment via robust recovery of low-rank tensors publication-title: Proceedings of Advances in Neural Information Processing Systems – start-page: 211 year: 2015 end-page: 220 ident: bib0039 article-title: Robust PCA via nonconvex rank approximation publication-title: 2015 IEEE International Conference on Data Mining – volume: 24 start-page: 2502 year: 2015 end-page: 2514 ident: bib0005 article-title: Background subtraction based on low-rank and structured sparse decomposition publication-title: IEEE Trans. Image Process. – start-page: 213 year: 2009 end-page: 216 ident: bib0015 article-title: Fast algorithms for recovering a corrupted low-rank matrix publication-title: 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) – reference: Z. Zhou, Y. Ma, Comments on efficient singular value thresholding computation, 2020. Available: – volume: 106 start-page: 337 year: 2000 end-page: 356 ident: bib0054 article-title: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities publication-title: J. Optim. Theory Appl. – start-page: 1432 year: 2021 end-page: 1436 ident: bib0006 article-title: A deep-unfolded reference-based RPCA network for video foreground-background separation publication-title: 2020 28th European Signal Processing Conference (EUSIPCO) – volume: 25 start-page: 829 year: 2016 end-page: 839 ident: bib0018 article-title: Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm publication-title: IEEE Trans. Image Process. – year: 2016 ident: bib0004 article-title: Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing – volume: 356 start-page: 10138 year: 2019 end-page: 10154 ident: bib0027 article-title: Generalized singular value thresholding operator based nonconvex low-rank and sparse decomposition for moving object detection publication-title: J. Franklin Inst. – volume: 58 start-page: 2643 year: 2015 end-page: 2654 ident: bib0042 article-title: Stable recovery of low-rank matrix via nonconvex schatten publication-title: Sci. China Math. – volume: 10 start-page: 74 year: 2017 end-page: 110 ident: bib0025 article-title: Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction publication-title: SIAM J. Imaging Sci. – volume: 99 start-page: 287 year: 2015 end-page: 325 ident: bib0055 article-title: Linearized alternating direction method with parallel splitting and adaptive penalty for separable convex programs in machine learning publication-title: Mach. Learn. – start-page: 1362 year: 2014 end-page: 1368 ident: bib0058 article-title: Hybrid singular value thresholding for tensor completion publication-title: Proceedings of the AAAI Conference on Artificial Intelligence – volume: 357 start-page: 6370 year: 2020 end-page: 6405 ident: bib0030 article-title: Nonconvex nonsmooth low-rank minimization for generalized image compressed sensing via group sparse representation publication-title: J. Franklin Inst. – start-page: 1673 year: 2011 end-page: 1680 ident: bib0007 article-title: Image classification by non-negative sparse coding, low-rank and sparse decomposition publication-title: CVPR 2011 – year: 2022 ident: bib0041 article-title: Truncated publication-title: Multimed. Tools Appl. – volume: 30 start-page: 1497 year: 2020 end-page: 1510 ident: bib0024 article-title: Robust PCA using generalized nonconvex regularization publication-title: IEEE Trans. Circuits Syst. Video Technol. – volume: 41 start-page: 250 year: 2020 end-page: 258 ident: bib0026 article-title: Video foreground-background separation based on generalized nonconvex robust principal component analysis publication-title: Chinese J. Sci. Instrum. – start-page: 1493 year: 2009 end-page: 1498 ident: bib0011 article-title: Sparse and low-rank matrix decompositions publication-title: Proceedings of the 15th IFAC Symposium on System Identification – volume: 21 start-page: 576 year: 2016 end-page: 583 ident: bib0035 article-title: Robust principal component analysis via truncated nuclear norm minimization publication-title: J. Shanghai Jiaotong University (Sci.) – reference: Z. Lin, M. Chen, Y. Ma, The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices, (2010). Available: – year: 2015 ident: bib0059 article-title: Understanding Analysis – reference: . – start-page: 387 year: 2014 end-page: 394 ident: bib0062 article-title: CDnet 2014: an expanded change detection benchmark dataset publication-title: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops – volume: 121 start-page: 183 year: 2017 end-page: 208 ident: bib0036 article-title: Weighted nuclear norm minimization and its applications to low level vision publication-title: Int. J. Comput. Vis. – volume: 58 start-page: 11 year: 2011 ident: bib0001 article-title: Robust principal component analysis? publication-title: J. ACM – volume: 6 start-page: 56945 year: 2018 end-page: 56953 ident: bib0028 article-title: Alternating direction method of multipliers for sparse and low-rank decomposition based on nonconvex nonsmooth weighted nuclear norm publication-title: IEEE Access – volume: 122 start-page: 22 year: 2014 end-page: 34 ident: bib0003 article-title: Robust PCA via principal component pursuit: a review for a comparative evaluation in video surveillance publication-title: Comput. Vis. Image Underst. – volume: 68 start-page: 6128 year: 2020 end-page: 6141 ident: bib0049 article-title: Best pair formulation & accelerated scheme for non-convex principal component pursuit publication-title: IEEE Trans. Signal Process. – volume: 20 start-page: 685 year: 2019 end-page: 717 ident: bib0046 article-title: Accelerated alternating projections for robust principal component analysis publication-title: J. Mach. Learn. Res. – volume: vol. 84 start-page: 1097 year: 2018 end-page: 1107 ident: bib0047 article-title: A unified framework for nonconvex low-rank plus sparse matrix recovery publication-title: Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics – volume: 20 start-page: 5845 year: 2020 end-page: 5854 ident: bib0009 article-title: A low-rank and sparse decomposition-based method of improving the accuracy of sub-pixel grayscale centroid extraction for spot images publication-title: IEEE Sens. J. – start-page: 4130 year: 2014 end-page: 4137 ident: bib0017 article-title: Generalized nonconvex nonsmooth low-rank minimization publication-title: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) – volume: 21 start-page: 576 issue: 5 year: 2016 ident: 10.1016/j.jfranklin.2022.09.002_bib0035 article-title: Robust principal component analysis via truncated nuclear norm minimization publication-title: J. Shanghai Jiaotong University (Sci.) doi: 10.1007/s12204-016-1765-5 – volume: 2014 start-page: 656074 year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0050 article-title: A generalized robust minimization framework for low-rank matrix recovery publication-title: Math. Probl. Eng. doi: 10.1155/2014/656074 – volume: 34 start-page: 2233 issue: 11 year: 2012 ident: 10.1016/j.jfranklin.2022.09.002_bib0065 article-title: RASL: robust alignment by sparse and low-rank decomposition for linearly correlated images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2011.282 – volume: 38 start-page: 744 issue: 4 year: 2016 ident: 10.1016/j.jfranklin.2022.09.002_bib0033 article-title: Partial sum minimization of singular values in robust PCA: algorithm and applications publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2015.2465956 – volume: 356 start-page: 10138 issue: 16 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0027 article-title: Generalized singular value thresholding operator based nonconvex low-rank and sparse decomposition for moving object detection publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2019.09.017 – volume: 20 start-page: 5845 issue: 11 year: 2020 ident: 10.1016/j.jfranklin.2022.09.002_bib0009 article-title: A low-rank and sparse decomposition-based method of improving the accuracy of sub-pixel grayscale centroid extraction for spot images publication-title: IEEE Sens. J. doi: 10.1109/JSEN.2020.2974725 – start-page: 1468 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0048 article-title: A nonconvex projection method for robust PCA – volume: 60 start-page: 5810 issue: 11 year: 2012 ident: 10.1016/j.jfranklin.2022.09.002_bib0020 article-title: Nonconvex splitting for regularized low-rank + sparse decomposition publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2012.2208955 – ident: 10.1016/j.jfranklin.2022.09.002_bib0057 – volume: 25 start-page: 4842 issue: 10 year: 2016 ident: 10.1016/j.jfranklin.2022.09.002_bib0038 article-title: Weighted schatten p-norm minimization for image denoising and background subtraction publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2016.2599290 – volume: 6 start-page: 69883 year: 2018 ident: 10.1016/j.jfranklin.2022.09.002_bib0022 article-title: A survey on nonconvex regularization-based sparse and low-rank recovery in signal processing, statistics, and machine learning publication-title: IEEE Access, doi: 10.1109/ACCESS.2018.2880454 – volume: 356 start-page: 2353 issue: 4 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0029 article-title: Multiple-prespecified-dictionary sparse representation for compressive sensing image reconstruction with nonconvex regularization publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2018.12.013 – volume: 106 start-page: 337 issue: 2 year: 2000 ident: 10.1016/j.jfranklin.2022.09.002_bib0054 article-title: Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1004603514434 – start-page: 211 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0039 article-title: Robust PCA via nonconvex rank approximation – ident: 10.1016/j.jfranklin.2022.09.002_bib0016 – start-page: 1432 year: 2021 ident: 10.1016/j.jfranklin.2022.09.002_bib0006 article-title: A deep-unfolded reference-based RPCA network for video foreground-background separation – volume: 109 start-page: 415 issue: 2 year: 2001 ident: 10.1016/j.jfranklin.2022.09.002_bib0056 article-title: Decomposition method with a variable parameter for a class of monotone variational inequality problems publication-title: J. Optim. Theory Appl. doi: 10.1023/A:1017522623963 – volume: 9 start-page: 167 issue: 1 year: 2013 ident: 10.1016/j.jfranklin.2022.09.002_bib0014 article-title: Sparse and low-rank matrix decomposition via alternating direction method publication-title: Pacific J. Optim. – volume: 47 start-page: 36 issue: 2 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0008 article-title: Low-rank modeling and its applications in image analysis publication-title: ACM Comput. Surv. doi: 10.1145/2674559 – volume: vol. 84 start-page: 1097 year: 2018 ident: 10.1016/j.jfranklin.2022.09.002_bib0047 article-title: A unified framework for nonconvex low-rank plus sparse matrix recovery – volume: 121 start-page: 183 issue: 2 year: 2017 ident: 10.1016/j.jfranklin.2022.09.002_bib0036 article-title: Weighted nuclear norm minimization and its applications to low level vision publication-title: Int. J. Comput. Vis. doi: 10.1007/s11263-016-0930-5 – volume: 25 start-page: 829 issue: 2 year: 2016 ident: 10.1016/j.jfranklin.2022.09.002_bib0018 article-title: Nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2015.2511584 – volume: 58 start-page: 30 issue: 1 year: 2004 ident: 10.1016/j.jfranklin.2022.09.002_bib0052 article-title: A tutorial on MM algorithms publication-title: Am. Stat. doi: 10.1198/0003130042836 – volume: 96 start-page: 1348 issue: 456 year: 2001 ident: 10.1016/j.jfranklin.2022.09.002_bib0061 article-title: Variable selection via nonconcave penalized likelihood and its oracle properties publication-title: J. Am. Stat. Assoc. doi: 10.1198/016214501753382273 – year: 2009 ident: 10.1016/j.jfranklin.2022.09.002_bib0002 article-title: Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization – volume: 40 start-page: 1935 issue: 4 year: 2012 ident: 10.1016/j.jfranklin.2022.09.002_bib0010 article-title: Latent variable graphical model selection via convex optimization publication-title: Ann. Stat. – volume: 122 start-page: 22 year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0003 article-title: Robust PCA via principal component pursuit: a review for a comparative evaluation in video surveillance publication-title: Comput. Vis. Image Underst. doi: 10.1016/j.cviu.2013.11.009 – volume: 283 start-page: 205 year: 2018 ident: 10.1016/j.jfranklin.2022.09.002_bib0043 article-title: Robust principal component analysis via optimal mean by joint ℓ2,1 and schatten p-norms minimization publication-title: Neurocomputing doi: 10.1016/j.neucom.2017.12.034 – start-page: 33 year: 2011 ident: 10.1016/j.jfranklin.2022.09.002_bib0044 article-title: GoDec: randomized low-rank & sparse matrix decomposition in noisy case – volume: 99 start-page: 287 issue: 2 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0055 article-title: Linearized alternating direction method with parallel splitting and adaptive penalty for separable convex programs in machine learning publication-title: Mach. Learn. doi: 10.1007/s10994-014-5469-5 – year: 2016 ident: 10.1016/j.jfranklin.2022.09.002_bib0004 – year: 1976 ident: 10.1016/j.jfranklin.2022.09.002_bib0060 – year: 2022 ident: 10.1016/j.jfranklin.2022.09.002_bib0041 article-title: Truncated γ norm-based low-rank and sparse decomposition publication-title: Multimed. Tools Appl. doi: 10.1007/s11042-022-12509-8 – volume: 10 start-page: 74 issue: 1 year: 2017 ident: 10.1016/j.jfranklin.2022.09.002_bib0025 article-title: Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction publication-title: SIAM J. Imaging Sci. doi: 10.1137/15M1027528 – volume: 68 start-page: 6128 year: 2020 ident: 10.1016/j.jfranklin.2022.09.002_bib0049 article-title: Best pair formulation & accelerated scheme for non-convex principal component pursuit publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2020.3011024 – volume: 43 start-page: 238 issue: 1 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0063 article-title: Robust low-rank tensor recovery with rectification and alignment publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/TPAMI.2019.2929043 – volume: 30 start-page: 1497 issue: 6 year: 2020 ident: 10.1016/j.jfranklin.2022.09.002_bib0024 article-title: Robust PCA using generalized nonconvex regularization publication-title: IEEE Trans. Circuits Syst. Video Technol. doi: 10.1109/TCSVT.2019.2908833 – volume: 58 start-page: 11 issue: 3 year: 2011 ident: 10.1016/j.jfranklin.2022.09.002_bib0001 article-title: Robust principal component analysis? publication-title: J. ACM doi: 10.1145/1970392.1970395 – volume: 3 start-page: 1 issue: 1 year: 2011 ident: 10.1016/j.jfranklin.2022.09.002_bib0031 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers publication-title: Found. Trends Mach. Learn. doi: 10.1561/2200000016 – volume: 85 start-page: 10 year: 2017 ident: 10.1016/j.jfranklin.2022.09.002_bib0032 article-title: Recovering low-rank and sparse matrix based on the truncated nuclear norm publication-title: Neural Netw. doi: 10.1016/j.neunet.2016.09.005 – volume: 20 start-page: 685 issue: 1 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0046 article-title: Accelerated alternating projections for robust principal component analysis publication-title: J. Mach. Learn. Res. – volume: 357 start-page: 6370 issue: 10 year: 2020 ident: 10.1016/j.jfranklin.2022.09.002_bib0030 article-title: Nonconvex nonsmooth low-rank minimization for generalized image compressed sensing via group sparse representation publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2020.03.032 – start-page: 4130 year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0017 article-title: Generalized nonconvex nonsmooth low-rank minimization – start-page: 1637 year: 2013 ident: 10.1016/j.jfranklin.2022.09.002_bib0064 article-title: Simultaneous rectification and alignment via robust recovery of low-rank tensors – volume: 6 start-page: 56945 year: 2018 ident: 10.1016/j.jfranklin.2022.09.002_bib0028 article-title: Alternating direction method of multipliers for sparse and low-rank decomposition based on nonconvex nonsmooth weighted nuclear norm publication-title: IEEE Access doi: 10.1109/ACCESS.2018.2872688 – start-page: 1362 year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0058 article-title: Hybrid singular value thresholding for tensor completion – volume: 24 start-page: 2502 issue: 8 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0005 article-title: Background subtraction based on low-rank and structured sparse decomposition publication-title: IEEE Trans. Image Process. doi: 10.1109/TIP.2015.2419084 – volume: 108 start-page: 425 issue: 2 year: 2021 ident: 10.1016/j.jfranklin.2022.09.002_bib0013 article-title: Estimating differential latent variable graphical models with applications to brain connectivity publication-title: Biometrika doi: 10.1093/biomet/asaa066 – volume: 10 start-page: 1341 issue: 6 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0034 article-title: Adaptive algorithms for low-rank and sparse matrix recovery with truncated nuclear norm publication-title: Int. J. Mach. Learn. Cybern. doi: 10.1007/s13042-018-0814-9 – start-page: 387 year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0062 article-title: CDnet 2014: an expanded change detection benchmark dataset – start-page: 1673 year: 2011 ident: 10.1016/j.jfranklin.2022.09.002_bib0007 article-title: Image classification by non-negative sparse coding, low-rank and sparse decomposition – year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0045 article-title: Non-convex robust PCA – start-page: 311 year: 2013 ident: 10.1016/j.jfranklin.2022.09.002_bib0021 article-title: Robust principal component analysis via capped norms – start-page: 213 year: 2009 ident: 10.1016/j.jfranklin.2022.09.002_bib0015 article-title: Fast algorithms for recovering a corrupted low-rank matrix – volume: 48 start-page: 3135 issue: 10 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0051 article-title: Visual data denoising with a unified schatten-p norm and ℓq norm regularized principal component pursuit publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2015.01.024 – volume: 100 start-page: 901 issue: 4 year: 2013 ident: 10.1016/j.jfranklin.2022.09.002_bib0053 article-title: Reduced rank regression via adaptive nuclear norm penalization publication-title: Biometrika doi: 10.1093/biomet/ast036 – year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0059 – start-page: 2862 year: 2014 ident: 10.1016/j.jfranklin.2022.09.002_bib0037 article-title: Weighted nuclear norm minimization with application to image denoising – volume: 21 start-page: 572 issue: 2 year: 2011 ident: 10.1016/j.jfranklin.2022.09.002_bib0012 article-title: Rank-sparsity incoherence for matrix decomposition publication-title: SIAM J. Optim. doi: 10.1137/090761793 – volume: 41 start-page: 250 issue: 1 year: 2020 ident: 10.1016/j.jfranklin.2022.09.002_bib0026 article-title: Video foreground-background separation based on generalized nonconvex robust principal component analysis publication-title: Chinese J. Sci. Instrum. – start-page: 1805 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0019 article-title: Generalized singular value thresholding – volume: 67 start-page: 5402 issue: 20 year: 2019 ident: 10.1016/j.jfranklin.2022.09.002_bib0023 article-title: Nonconvex regularized robust PCA using the proximal block coordinate descent algorithm publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2019.2940121 – year: 2022 ident: 10.1016/j.jfranklin.2022.09.002_bib0040 article-title: Moving object detection via RPCA framework using non-convex low-rank approximation and total variational regularization publication-title: Signal Image Video Process. – volume: 58 start-page: 2643 issue: 12 year: 2015 ident: 10.1016/j.jfranklin.2022.09.002_bib0042 article-title: Stable recovery of low-rank matrix via nonconvex schatten p-minimization publication-title: Sci. China Math. doi: 10.1007/s11425-015-5081-6 – start-page: 1493 year: 2009 ident: 10.1016/j.jfranklin.2022.09.002_bib0011 article-title: Sparse and low-rank matrix decompositions |
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