A separable surrogate function method for sparse and low-rank matrices decomposition

References

• Tomasi C, Kanade T. Shape and motion from image streams under orthography: a factorization method. Int J Comput Vis. 1992;9:137–154. doi: 10.1007/BF00129684
   Web of Science ®Google Scholar
• Chen P, Suter D. Recovering the missing components in a large noisy low-rank matrix: application to SFM. IEEE Trans Pattern Anal Mach Intell. 2004;26:1051–1063. doi: 10.1109/TPAMI.2004.52
   PubMed Web of Science ®Google Scholar
• Wright J, Ganesh A, Rao S. Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices. version2, 2009; 1–44. https://arxiv.org/abs/0905.0233.
   Google Scholar
• Deerwester S, Dumains ST, Landauer T, et al. Indexing by latent semantic analysis. J Soc Inf Sci. 1990;41:391–407. doi: 10.1002/(SICI)1097-4571(199009)41:6<391::AID-ASI1>3.0.CO;2-9
   Web of Science ®Google Scholar
• Papadimitriou C, Raghavan P, Tamaki H, et al. Latent semantic indexing, a probabilistic analysis. J Comput Syst Sci. 2000;61:217–235. doi: 10.1006/jcss.2000.1711
   Web of Science ®Google Scholar
• Argyriou A, Evgeniou T, Pontil M. Multi-task feature learning. Adv Neural Inf Process Syst. 2007;19:41–48.
   Google Scholar
• Abernethy J, Bach F, Evgeniou T, et al. Low-rank matrix factorization with attributes. arXiv Preprint cs/0611124, 2006.
   Google Scholar
• Amit Y, Fink M, Srebro N. Uncovering shared structures in multiclass classification. In: Proceedings of the 24th International Conference on Machine Learning; Providence, RI: ACM. Corvallis, Oregon, USA; 2007. 17–24.
   Google Scholar
• Zhang H, Lin Z, Zhang C, et al. Robust latent low rank representation for subspace clustering. Neurocomputing. 2014;145:369–373. doi: 10.1016/j.neucom.2014.05.022
   Web of Science ®Google Scholar
• Bai J, Li J, Deng J. A class of multilevel structured low-rank approximation arising in material processing. Int J Comput Math. 2016;95(2):329–340. doi: 10.1080/00207160.2017.1285020
   Web of Science ®Google Scholar
• Mesbahi M, Papavassilopoulos GP. On the rank minimization problem over a positive semidefinitelinear matrix inequality. IEEE Trans Autom Control. 1997;42:239–243. doi: 10.1109/9.554402
   Web of Science ®Google Scholar
• Eckart C, Young G. The approximation of one matrix by another of lower rank. Psychometrika. 1936;1:211–218. doi: 10.1007/BF02288367
   Google Scholar
• Li J, Liu Z, Li G. Lower bounds for the low-rank matrix approximation. J Inequalities Appl. 2017;288:1–14.
   Google Scholar
• Jolliffe I. Principal component analysis. New York, USA: Springer-Verlag; 1986.
   Google Scholar
• Yuan X, Yang J. Sparse and low-rank matrix decomposition via alternating direction methods. Pac J Optim. 2013;9:167–180.
   Web of Science ®Google Scholar
• Lin Z, Chen M, Ma Y. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. version 3 2013: Available from: http://arxiv.org/abs/1009.5055.
   Google Scholar
• Lin Z, Ganesh A, Wright J, et al. Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. J Mar Biol Assoc UK. 2009;56(3):707–722.
   Google Scholar
• Daubechies I, Defrise M, De-Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm Pure Appl Math. 2004;LVII:1413-–1457. doi: 10.1002/cpa.20042
   Google Scholar
• Candès EJ, Li X, Ma Y, et al. Robust principal component analysis? J ACM (JACM). 2011;58:1–37. doi: 10.1145/1970392.1970395
   Web of Science ®Google Scholar
• Cai J-F, Candès EJ, Shen Z. A singular value thresholding algorithm for matrix completion. SIAM J Optim. 2010;20:1956–1982. doi: 10.1137/080738970
   Web of Science ®Google Scholar
• Tao M, Yuan X. Recovering low-rank and sparse components of matrices from incomplete and noisy observations. SIAM J Optim. 2011;20:57–81. doi: 10.1137/100781894
   Google Scholar
• Chandrasekaran V, Sanghavi S, Parrilo PA, et al. Rank-sparsity incoherence for matrix decomposition. SIAM J Optim. 2011;21:572–596. doi: 10.1137/090761793
   Web of Science ®Google Scholar
• Candès EJ, Recht B. Exact matrix completion via convex optimization. Found Comput Math. 2009;9:717–772. doi: 10.1007/s10208-009-9045-5
   Web of Science ®Google Scholar
• Recht B, Fazel M, Parrilo PA. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 2010;52:471–501. doi: 10.1137/070697835
   Web of Science ®Google Scholar
• Candès EJ, Plan Y. Matrix completion with noise. Proc IEEE. 2010;98:925–936. doi: 10.1109/JPROC.2009.2035722
   Web of Science ®Google Scholar
• Ma S, Goldfarb D, Chen L. Fixed point and Bregman iterative methods for matrix rank minimization. Math Program. 2011;128:321–353. doi: 10.1007/s10107-009-0306-5
   Web of Science ®Google Scholar
• Bertsekas D. Constrained optimization and Lagrange multiplier method. New York: Academic Press; 1982.
   Google Scholar
• Chan RH, Yang J, Yuan X. Alternating direction method for image inpainting in wavelet domains. SIAM J Imaging Sci. 2011;4:807–826. doi: 10.1137/100807247
   Web of Science ®Google Scholar
• Chan C, Chan RH, Ma S, et al. Inertial proximal ADMM for linearly constrained separable convex optimization. SIAM J Imaging Sci. 2015;8:2239–2267. doi: 10.1137/15100463X
   Web of Science ®Google Scholar
• He BS, Yang H. A new inexact alternating directions method for monontone variational inequalities. Math Program. 2002;92:103–118. doi: 10.1007/s101070100280
   Web of Science ®Google Scholar
• He BS, Yang H. Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities. Oper Res Lett. 1998;23:151–161. doi: 10.1016/S0167-6377(98)00044-3
   Web of Science ®Google Scholar
• He BS, Yuan X. The unified framework of some proximal-based decomposition methods for monotone variational inequalities with separable structure. Pac J Optim. 2012;8:817–844.
   Web of Science ®Google Scholar
• Duong VT, Dang VH. Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems. Optimization. 2018;67(1):83–102. doi: 10.1080/02331934.2017.1377199
   Web of Science ®Google Scholar
• Kontogiorgis S, Meyer RR. A variable-penalty alternating directions method for convex optimization. Math Program. 1998;83:29–53.
   Web of Science ®Google Scholar
• Netrapalli P, Niranjan UN, Sanghavi S, et al. Provable non-convex robust PCA. Adv Neural Inf Process Syst. 2014;2:1107–1115.
   Google Scholar
• Liu Z, Li J, Li G, et al. A new model for sparse and low-rank matrix decomposition. J Appl Anal Comput. 2017;2:600–617.
   Google Scholar
• Combettes PL, Pesquet JC. Proximal thresholding algorithm for minimization over orthonormal bases. SIAM J Optim. 2007;18:1351–1376. doi: 10.1137/060669498
   Web of Science ®Google Scholar
• Elad M. Why simple shrinkage is still relevant for redundant representations? IEEE Trans Inf Theory. 2006;52:5559–5569. doi: 10.1109/TIT.2006.885522
   Web of Science ®Google Scholar
• Hale ET, Yin W, Zhang Y. Fixed-point continuation for ℓ1 -minimization: methodology and convergence. SIAM J Optim. 2008;19(3):1107–1130. doi: 10.1137/070698920
   Web of Science ®Google Scholar
• Tseng P. On accelerated proximal gradient methods for convex-concave optimization. Washington, DC: University of Washington. 2008.
   Google Scholar