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Mutual-manifold regularized robust fast latent LRR for subspace recovery and learning

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Abstract

In this paper, we propose a simple yet effective low-rank representation (LRR) and subspace recovery model called mutual-manifold regularized robust fast latent LRR. Our model improves the representation ability and robustness from twofold. Specifically, our model is built on the Frobenius norm-based fast latent LRR decomposing given data into a principal feature part, a salient feature part and a sparse error, but improves it clearly by designing mutual-manifold regularization to encode, preserve and propagate local information between coefficients and salient features. The mutual-manifold regularization is defined by using the coefficients as the adaptive reconstruction weights for salient features and constructing a Laplacian matrix over salient features for the coefficients. Thus, some important local topology structure information can be propagated between them, which can make the discovered subspace structures and features potentially more accurate for the data representations. Besides, our approach also considers to improve the robust properties of subspace recovery against noise and sparse errors in coefficients, which is realized by decomposing original coefficients matrix into an error-corrected part and a sparse error part fitting noise in coefficients, and the recovered coefficients are then used for robust subspace recovery. Experimental results on several public databases demonstrate that our method can outperform other related algorithms.

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References

  1. Liu G, Lin Z, Yu Y, Tang X (2010) Unsupervised object segmentation with a hybrid graph model (HGM). IEEE Trans Pattern Anal Mach Intell 32(5):910–924

    Article  Google Scholar 

  2. Kanatani K (2001) Motion segmentation by subspace separation and model selection. In: Proceedings eighth IEEE international conference on computer vision, ICCV 2001, 2001, vol. 2, pp 586–591

  3. Hong W, Wright J, Huang K, Ma Y (2006) Multiscale hybrid linear models for lossy image representation. IEEE Trans Image Process 15(12):3655–3671

    Article  MathSciNet  Google Scholar 

  4. Vidal R, Ma Y, Sastry S (2005) Generalized principal component analysis (GPCA). IEEE Trans Pattern Anal Mach Intell 27(12):1945–1959

    Article  Google Scholar 

  5. Rao S, Tron R, Vidal R, Ma Y (2010) Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE Trans Pattern Anal Mach Intell 32(10):1832–1845

    Article  Google Scholar 

  6. Yang AY, Wright J, Ma Y, Sastry SS (2008) Unsupervised segmentation of natural images via lossy data compression. Comput Vis Image Underst 110(2):212–225

    Article  Google Scholar 

  7. Jolliffe I (2011) Principal component analysis. Springer, Berlin

    MATH  Google Scholar 

  8. 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(1):171–184

    Article  Google Scholar 

  9. Vidal R (2011) Subspace clustering. IEEE Signal Process Mag 28(2):52–68

    Article  Google Scholar 

  10. Candès EJ, Li X, Ma Y, Wright J (2011) Robust principal component analysis. J ACM 58(3):11:1–11:37

    Article  MathSciNet  Google Scholar 

  11. Zhang Z, Li F, Zhao M, Zhang L, Yan S (2017) Robust neighborhood preserving projection by nuclear/L2,1-norm regularization for image feature extraction. IEEE Trans Image Process 26(4):1607–1622

    Article  MathSciNet  Google Scholar 

  12. Liu G, Zhang Z, Liu Q, Xiong H (2019) Robust subspace clustering with compressed data. IEEE Trans Image Process 28(10):5161–5170

    Article  MathSciNet  Google Scholar 

  13. Wang L, Wang B, Zhang Z, Ye Q, Fu L, Liu G, Wang M (2019) Robust auto-weighted projective low-rank and sparse recovery for visual representation. Neural Netw 117:201–215

    Article  Google Scholar 

  14. Zhang Z, Zhao M, Li F, Zhang L, Yan S (2017) Robust alternating low-rank representation by joint Lp- and L2, p-norm minimization. Neural Netw 96:55–70

    Article  Google Scholar 

  15. Zhan S, Wu J, Han N, Wen J, Fang X (2019) Unsupervised feature extraction by low-rank and sparsity preserving embedding. Neural Netw 109:56–66

    Article  Google Scholar 

  16. Wu J, Guo A, Sheng VS, Zhao P, Cui Z, Li H (2017) Adaptive Low-rank multi-label active learning for image classification. In: Proceedings of ACM international conference on multimedia, pp 1336–1344

  17. Zhang Z, Ren J, Li S, Hong R, Zha Z, Wang M (2019) Robust subspace discovery by block-diagonal adaptive locality-constrained representation. In: Proceedings of the ACM international conference on multimedia, Nice, France

  18. Zhang Z, Wang L, Li S, Wang Y, Zhang Z, Zha Z, Wang M (2019) Adaptive structure-constrained robust latent low-rank coding for image recovery. In: Proceedings of the 19th IEEE international conference on data mining, Beijing, China

  19. Jiang S, Ding Z, Fu Y (2017) Deep low-rank sparse collective factorization for cross-domain recommendation. In: Proceedings of ACM international conference on multimedia, pp 163–171

  20. Wang Y, Lin X, Wu L, Zhang W, Zhang Q (2004) Exploiting correlation consensus: towards subspace clustering for multi-modal data. In: Proceedings of ACM international conference on multimedia, pp 981–984

  21. Chiang K, Dhillon IS, Hsieh C (2018) Using side information to reliably learn low-rank matrices from missing and corrupted observations. J Mach Learn Res 19:76:1–76:35

    MathSciNet  MATH  Google Scholar 

  22. Liu G, Lin Z, Yu Y (2010) Robust Subspace segmentation by low-rank representation. In: Proceedings of the 27th international conference on machine learning (ICML-10), 2010, pp 663–670

  23. Liu G, Yan S (2011) Latent low-rank representation for subspace segmentation and feature extraction. In: Proceedings of the international conference on computer vision, 2011, pp 1615–1622

  24. Lin Z, Chen M, Ma Y (2009) The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. eprint arXiv 2009

  25. Zhang H, Zhang Y, Xi P (2014) fLRR: fast low-rank representation using Frobenius-norm. Electron Lett 50(13):936–938

    Article  Google Scholar 

  26. Song Y, Wu Y (2018) Subspace clustering based on latent low rank representation with Frobenius norm minimization. Neurocomputing 275:2479–2489

    Article  Google Scholar 

  27. Zhang Z, Yan S, Zhao M (2014) Similarity preserving low-rank representation for enhanced data representation and effective subspace learning. Neural Netw 53:81–94

    Article  Google Scholar 

  28. Wang L, Zhang Z, Li S, Liu G, Hou C, Qin J (2018) “Similarity-Adaptive latent low-rank representation for robust data representation”, in PRICAI. Trends Artif Intell 2018:71–84

    Google Scholar 

  29. Nefian AV (2002) Embedded Bayesian networks for face recognition. In: Proceedings of IEEE international conference on multimedia and expo, 2002, vol 2, pp 133–136

  30. Lee KC, Ho J, Kriegman DJ (2005) Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans Pattern Anal Mach Intell 5:684–698

    Google Scholar 

  31. Martínez A, Benavente R (1998) The AR face database. CVC Technical Report #24, 1998

  32. Samaria FS, Harter AC (1994) Parameterisation of a stochastic model for human face identification. In: Proceedings of 1994 IEEE workshop on applications of computer vision, 1994, pp 138–142

  33. Nene SA, Nayar SK, Murase H (1996) Columbia object image library (coil-20). Technical Report CUCS-005-96

  34. LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324

    Article  Google Scholar 

  35. Hull JJ (1994) A database for handwritten text recognition research. IEEE Trans Pattern Anal Mach Intell 16(5):550–554

    Article  Google Scholar 

  36. Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905

    Article  Google Scholar 

  37. Bao BK, Liu G, Xu C, Yan S (2012) Inductive robust principal component analysis. IEEE Trans Image Process 21(8):3794–3800

    Article  MathSciNet  Google Scholar 

  38. Zhang Z, Li F, Zhao M, Zhang L, Yan S (2016) Joint low-rank and sparse principal feature coding for enhanced robust representation and visual classification. IEEE Trans Image Process 25(6):2429–2443

    Article  MathSciNet  Google Scholar 

  39. Lu C, Min H, Zhao Z, Zhu L, Huang D, Yan S (2012) Robust and efficient subspace segmentation via least squares regression. ECCV 2012:347–360

    Google Scholar 

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Acknowledgements

The authors would like to express sincere thanks to reviewers for their insightful comments, making our manuscript a higher standard. This work is partially supported by National Natural Science Foundation of China (61672365, 61502238, 61622305, 61432019 and 61772171) and the Fundamental Research Funds for the Central Universities of China (JZ2019HGPA0102).

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Authors and Affiliations

  1. School of Computer Science and Technology, Soochow University, Suzhou, 215006, China

    Xianzhen Li, Zhao Zhang & Li Zhang

  2. Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing, 210023, China

    Li Zhang

  3. Key Laboratory of Knowledge Engineering with Big Data (Ministry of Education) and School of Computer Science and Information Engineering, Hefei University of Technology, Hefei, China

    Zhao Zhang & Meng Wang

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  1. Xianzhen Li
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  2. Zhao Zhang
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  3. Li Zhang
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  4. Meng Wang
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Correspondence to Zhao Zhang.

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Li, X., Zhang, Z., Zhang, L. et al. Mutual-manifold regularized robust fast latent LRR for subspace recovery and learning. Neural Comput & Applic 32, 13363–13376 (2020). https://doi.org/10.1007/s00521-019-04688-7

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  • DOI: https://doi.org/10.1007/s00521-019-04688-7

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