Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 69, 2020 - Issue 5
162
Views
1
CrossRef citations to date
0
Altmetric
Articles

A splitting method for the locality regularized semi-supervised subspace clustering

, & ORCID Icon
Pages 1069-1096 | Received 16 Oct 2018, Accepted 09 Sep 2019, Published online: 08 Oct 2019

References

  • Chapelle O, Schölkopf B, Zien A. Semi-supervised learning. Cambridge (MA): The MIT Press; 2006.
  • Rosenberg C, Hebert M, Schneiderman H. Semi-supervised self-training of object detection models. Proceedings of the 7th IEEE Workshops on Application of Computer Vision; Vol. 1; 2005 Jan 5–7; Breckenridge, CO, USA; 2005. p. 29–36.
  • Blum A, Mitchell T. Combining labeled and unlabeled data with co-training. Proceedings of the Eleventh Annual Conference on Computational Learning Theory; 1998 Jul 24–26; Madison, WI, USA; 1998. p. 92–100.
  • Astorino A, Gorgone E, Gaudioso M, et al. Data preprocessing in semi-supervised SVM classification. Optimization. 2011;60(1–2):143–151. doi: 10.1080/02331931003692557
  • Bai YQ, Niu BL, Chen Y. New SDP models for protein homology detection with semi-supervised SVM. Optimization. 2013;62(4):561–572. doi: 10.1080/02331934.2011.611515
  • Liang RL, Bai YQ, Lin HX. An inexact splitting method for the subspace segmentation from incomplete and noisy observations. J Global Optim. 2019;73(2):411–429. doi: 10.1007/s10898-018-0684-4
  • Zhou DY, Bousquet O, Lal TN, et al. Learning with local and global consistency. Proceedings of the 16th International Conference on Neural Information Processing Systems; 2003 Dec 9–11. Cambridge (MA): MIT Press; 2003. p. 321–328.
  • Zhu XJ, Ghahramani ZB, Lafferty J. Semi-supervised learning using Gaussian fields and harmonic functions. Proceedings of the 20th International Conference on International Conference on Machine Learning; 2003 Aug 21–24; Washington, DC, USA; 2003. p. 912–919.
  • Zhuang LS, Gao HY, Lin ZC, et al. Non-negative low rank and sparse graph for semi-supervised learning. 2012 IEEE Conference on Computer Vision and Pattern Recognition; 2012 Jun 16–21. Providence (RI): IEEE; 2012. p. 2328–2335.
  • Wright J, Ma Y, Mairal J, et al. Sparse representation for computer vision and pattern recognition. Proc IEEE. 2010;98(6):1031–1044. doi: 10.1109/JPROC.2010.2044470
  • Yan SC, Wang H. Semi-supervised learning by sparse representation. Proceedings of the 2009 SIAM International Conference on Data Mining; 2009 Apr 30–May 2; Sparks, NV, USA; 2009. p. 792–801.
  • Liu GC, Lin ZC, Yan SC, et al. Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell. 2013;35(1):171–184. doi: 10.1109/TPAMI.2012.88
  • Cai D, He X, Han J, et al. Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell. 2011;33(8):1548–1560. doi: 10.1109/TPAMI.2010.231
  • Shang FH, Jiao LC, Wang F. Graph dual regularization non-negative matrix factorization for co-clustering. Pattern Recognit. 2012;45(6):2237–2250. doi: 10.1016/j.patcog.2011.12.015
  • Liu GC, Yan SC. Latent low-rank representation for subspace segmentation and feature extraction. Proceedings of the 2011 International Conference on Computer Vision; 2011 Nov 6–13; Barcelona, Spain; 2011. p. 1615–1622.
  • Fei LK, Xu Y, Fang XZ, et al. Low rank representation with adaptive distance penalty for semi-supervised subspace classification. Pattern Recognit. 2017;67(Supplement C):252–262. doi: 10.1016/j.patcog.2017.02.017
  • Li CG, Lin ZC, Zhang HG, et al. Learning semi-supervised representation towards a unified optimization framework for semi-supervised learning. Proceedings of the 2015 IEEE International Conference on Computer Vision; 2015 Dec 7–13; Santiago, Chile: IEEE; 2015. p. 2767–2775.
  • Gao QX, Liu JJ, Zhang HL, et al. Joint global and local structure discriminant analysis. IEEE Trans Inf Forensic Secur. 2013;8(4):626–635. doi: 10.1109/TIFS.2013.2246786
  • Zheng YG, Zhang XR, Yang SY, et al. Low-rank representation with local constraint for graph construction. Neurocomputing. 2013;122:398–405. doi: 10.1016/j.neucom.2013.06.013
  • Zheng M, Bu J, Chen C, et al. Graph regularized sparse coding for image representation. IEEE Trans Image Process. 2011;20(5):1327–1336. doi: 10.1109/TIP.2010.2090535
  • Chen JH, Ye JP, Li Q. Integrating global and local structures: a least squares framework for dimensionality reduction. Proceedings of the 2007 IEEE Conference on Computer Vision and Pattern Recognition; 2007 Jun 17–22; Minneapolis (MN): IEEE; 2007. p. 1–8.
  • Guan N, Tao D, Luo Z, et al. Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent. IEEE Trans Image Process. 2011;20(7):2030–2048. doi: 10.1109/TIP.2011.2105496
  • Yin M, Gao J, Lin Z. Laplacian regularized low-rank representation and its applications. IEEE Trans Pattern Anal Mach Intell. 2016;38(3):504–517. doi: 10.1109/TPAMI.2015.2462360
  • He BS, Yuan XM. Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming. Numer Algebra Control Optim. 2013;3(2):247–260. doi: 10.3934/naco.2013.3.247
  • Liu RS, Lin ZC, Su ZX. Linearized alternating direction method with parallel splitting and adaptive penalty for separable convex programs in machine learning. Proceedings of the 5th Asian Conference on Machine Learning; Vol. 29; 2013 Nov 13–15; Canberra, Australia; 2013. p. 1–16.
  • He BS, Tao M, Yuan XM. A splitting method for separable convex programming. IMA J Numer Anal. 2015;35(1):394–426. doi: 10.1093/imanum/drt060
  • Yang JF, Yin WT, Zhang Y, et al. A fast algorithm for edge-preserving variational multichannel image restoration. SIAM J Imaging Sci. 2009;2(2):569–592. doi: 10.1137/080730421
  • Cai JF, Candès EJ, Shen ZW. A singular value thresholding algorithm for matrix completion. SIAM J Optim. 2010;20(4):1956–1982. doi: 10.1137/080738970
  • Taylor AB, Hendrickx JM, Glineur F. Exact worst-case convergence rates of the proximal gradient method for composite convex minimization. J Optim Theory Appl. 2018;178(2):455–476. doi: 10.1007/s10957-018-1298-1
  • Toh KC, Yun S. An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems. Pac J Optim. 2010;6(3):615–640.
  • Bai YQ, Liang RL, Yang ZW. Splitting augmented Lagrangian method for optimization problems with a cardinality constraint and semicontinuous variables. Optim Methods Softw. 2016;31(5):1089–1109. doi: 10.1080/10556788.2016.1196206
  • Cheng HR, Deng W, Fu C, et al. Graph-based semi-supervised feature selection with application to automatic spam image identification. Computer Science for Environmental Engineering and EcoInformatics: International Workshop; 2011 Jul 29–31; Kunming, China; 2011. p. 259–264.
  • Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci. 2009;2(1):183–202. doi: 10.1137/080716542
  • He R, Zheng WS, Hu BG, et al. Nonnegative sparse coding for discriminative semi-supervised learning. Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition; 2011 Jun 20–25; Colorado Springs (CO): IEEE; 2011. p. 2849–2856.
  • Hoyer PO. Modeling receptive fields with non-negative sparse coding. Neurocomputing. 2003;52–54:547–552. doi: 10.1016/S0925-2312(02)00782-8
  • Fang XZ, Xu Y, Li XL, et al. Learning a nonnegative sparse graph for linear regression. IEEE Trans Image Process. 2015;24(9):2760–2771. doi: 10.1109/TIP.2015.2425545
  • Wang JD, Wang F, Zhang CS, et al. Linear neighborhood propagation and its applications. IEEE Trans Pattern Anal Mach Intell. 2009;31(9):1600–1615. doi: 10.1109/TPAMI.2008.216
  • Zheng ZL, Zhang JS, Zhu SH, et al. CUPID: consistent unlabeled probability of identical distribution for image classification. Knowl-Based Syst. 2017;137:115–122. doi: 10.1016/j.knosys.2017.09.019
  • Nie FP, Xu D, Tsang WH, et al. Flexible manifold embedding: a framework for semi-supervised and unsupervised dimension reduction. IEEE Trans Image Process. 2010;19(7):1921–1932. doi: 10.1109/TIP.2010.2044958
  • Shi JB, Malik J. Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell. 2000;22(8):888–905. doi: 10.1109/34.868688

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.