Abstract
Low-rank representation (LRR), which constructs a robust low rank representation for data processing, has attracted much attention in the past decades. It is assumed that the data points lie on a low-dimensional subspace and the representation matrix of the data points is low-rank. In real applications, the collected data might be corrupted by noises or errors. The low-rank learning methods can recover the noisy data and capture the global information of the data. In this chapter, we introduce the low-rank learning methods and their extensions. The main idea, objective function, and optimization of these methods are introduced in detail. Finally, we make a numerical experiment on two publicly image databases to verify the performance of these methods. It is shown that the LRE and LRLE converge very fast and obtain competitive performances against other methods. However, how to further increase performances is still a challenging problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bao B-K, Liu G, Xu C, Yan S (2012) Inductive robust principal component analysis. IEEE Trans Image Process 21:3794–3800
Bhardwaj A, Raman S (2016) Robust PCA-based solution to image composition using augmented Lagrange multiplier (ALM). Vis Comput 32:591–600
Cai J-F, Candes EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20:1956–1982
Chen Y, Lai Z, Wong W, Shen L, Hu Q (2018) Low-rank linear embedding for image recognition. IEEE Trans Multimedia 20:3212–3222
Guyon C, Bouwmans T, Zahzah EH (2012) Foreground detection via robust low rank matrix decomposition including spatio-temporal constraint. In: International workshop on background model challenges, vol 7728. ACCV
He X, Yan S, Hu Y, Niyogi P, Zhang H-J (2005b) Face recognition using Laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27:328–340
Ji H, Huang S-B, Shen Z, Xu Y (2011) Robust video restoration by joint sparse and low rank matrix approximation. SIAM J Imaging Sci 4:1122–1142
Kulis B, Surendran AC, Platt JC (2007) Fast low-rank semidefinite programming for embedding and clustering. In: International conference on artificial intelligence and statistics (AISTATS), pp 235–242
Li C-G, Qi X, Guo J (2013) Dimensionality reduction by low-rank embedding. Lect Notes Comput Sci 7751:181–188
Liu G, Lin Z (2010) Robust subspace segmentation by low-rank representation. In: Proceedings of international conference on machine learning
Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low rank representation. IEEE Trans Pattern Anal Mach Intell 35:171–184
Liu J, Chen Y, Zhang J, Xu Z (2014) Enhancing low-rank subspace clustering by manifold regularization. IEEE Trans Image Process 23:4022–4030
Lu Y, Lai Z, Xu Y, Li X, Zhang D, Yuan C (2015) Low-rank preserving projections. IEEE Trans Cybern 46:1900–1913
Nie F, Huang H, Cai X, Ding C (2010a) Efficient and robust feature selection via joint L2,1-norms minimization. In: Proceedings of advances in neural information processing systems, vol 23
Patel VM, Nguyen HV, Vidal R (2013) Latent space sparse subspace clustering. In: Proceedings of the IEEE international conference on computer vision, pp 225–232
Peng X, Yi Z, Tang H (2015) Robust subspace clustering via thresholding ridge regression. In: Twenty-ninth AAAI conference on artificial intelligence
Qiao L, Chen S, Tan X (2010) Sparsity preserving projections with applications to face recognition. Pattern Recogn 43(1):331–341
Tang J, Alelyani S, Liu H (2014) Feature selection for classification: a review. In: Data classification: algorithms and applications. CRC Press, pp 37–64
Wen J, Han N, Fang X, Fei L, Yan K, Zhan S (2018) Low-rank preserving projection via graph regularized reconstruction. IEEE Trans Cybern 49:1279–1291
Wong WK, Lai Z, Wen J, Fang X, Lu Y (2017) Low-rank embedding for robust image feature extraction. IEEE Trans Image Process 26:2905–2917
Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y (2009b) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31:210–227
Xue Y, Guo X, Cao X (2012) Motion saliency detection using low-rank and sparse decomposition. Spectrum
Yang J, Yin W, Zhang Y, Wang Y (2009) A fast algorithm for edge-preserving variational multihannel image restoration. SIAM J Imaging Sci 2:569–592
Yao Q, Kwok JT (2015) Colorization by patch-based local low-rank matrix completion. In: Proceedings of the 29th AAAI conference on artificial intelligence
You C, Robinson D, Vidal R (2016) Scalable sparse subspace clustering by orthogonal matching pursuit. In: Proceedings of the IEEE conference on computer vision and pattern recognition
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zhao, H., Lai, Z., Leung, H., Zhang, X. (2020). Low Rank Feature Learning. In: Feature Learning and Understanding. Information Fusion and Data Science. Springer, Cham. https://doi.org/10.1007/978-3-030-40794-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-40794-0_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-40793-3
Online ISBN: 978-3-030-40794-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)