Skip to main content
SpringerLink
Log in

Low-Rank Discriminative Adaptive Graph Preserving Subspace Learning

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

The global and local geometric structures of data play a key role in subspace learning. Although many manifold-based subspace learning methods have been proposed for preserving the local geometric structure of data, they usually use a predefined neighbor graph to characterize it. However, the predefined neighbor graph might be not optimal since it keeps fixed during the subsequent subspace learning process. Moreover, most manifold-based subspace learning methods ignore the global structure of data. To address these issues, we propose a low-rank discriminative adaptive graph preserving (LRDAGP) subspace learning method for image feature extraction and recognition by integrating the low-rank representation , adaptive manifold learning, and supervised regularizer into a unified framework. To capture the optimal local geometric structure of data for subspace learning, LRDAGP adopts an adaptive manifold learning strategy that the neighbor graph is adaptively updated during the subspace learning process. To capture the optimal global structure of data for subspace learning, LRDAGP also seeks the low-rank representations of data in a low-dimensional subspace during the subspace learning process. Moreover, for improving the discrimination ability of the learned subspace, a supervised regularizer is designed and incorporated into the LRDAGP model. Experimental results on several image datasets show that LRDAGP is effective for image feature extraction and recognition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86

    Article  Google Scholar 

  2. Belhumeur PN, Hespanha JP, Kriegman DJ (2013) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720

    Article  Google Scholar 

  3. Zhong F, Zhang J (2013) Linear discriminant analysis based on L1-norm maximization. IEEE Trans Image Process 22(8):3018–3027

    Article  MathSciNet  Google Scholar 

  4. Li X, Jiang T, Zhang K (2006) Efficient and robust feature extraction by maximum margin criterion. IEEE Trans Neural Netw 17(1):157–165

    Article  Google Scholar 

  5. Yang J, Zhang D, Frangi AF, Yang J (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans Pattern Anal Mach Intell 26(1):131–137

    Article  Google Scholar 

  6. Li M, Yuan B (2005) 2D-LDA: a statistical linear discriminant analysis for image matrix. Pattern Recogn Lett 26(5):527–532

    Article  Google Scholar 

  7. Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319–2323

    Article  Google Scholar 

  8. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Article  Google Scholar 

  9. Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396

    Article  Google Scholar 

  10. He X, Yan S, Hu Y, Niyogi P, Zhang H (2005) Face recognition using Laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340

    Article  Google Scholar 

  11. Yu W, Teng X, Liu C (2006) Face recognition using discriminant locality preserving projections. Image Vis Comput 24(3):239–248

    Article  Google Scholar 

  12. He X, Cai D, Yan S, Zhang H (2005) Neighborhood preserving embedding. In: Proceedings of 20th IEEE international conference on computer vision, pp 1208–1213

  13. Yan S, Xu D, Zhang B, Zhang H, Yang Q, Lin S (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40–51

    Article  Google Scholar 

  14. Zhu X, Li X, Zhang S (2016) Block-row sparse multiview multilabel learning for image classification. IEEE Trans Cybern 46(2):450–461

    Article  Google Scholar 

  15. Lai Z, Xu Y, Yang J, Shen L, Zhang D (2017) Rotational invariant dimensionality reduction algorithms. IEEE Trans Cybern 47(11):3733–3746

    Article  Google Scholar 

  16. Zhu X, Zhang S, He W, Hu R, Lei C, Zhu P (2019) One-step multi-view spectral clustering. IEEE Trans Knowl Data Eng 31(10):2022–2034

    Article  Google Scholar 

  17. Du H, Li G, Wang S, Zhang F (2019) Discriminant locality preserving projections based on \(l_{2, p}\)-norm for image feature extraction and recognition. J Vis Commun Image Represent 58:166–177

    Article  Google Scholar 

  18. Zhang L, Qiao L, Chen S (2010) Graph-optimized locality preserving projections. Pattern Recogn 43(6):1993–2002

    Article  Google Scholar 

  19. Zhang L, Chen S, Qiao L (2012) Graph optimization for dimensionality reduction with sparsity constraints. Pattern Recogn 45(3):1205–1210

    Article  Google Scholar 

  20. Nie F, Wang X, Huang H (2014) Clustering and projected clustering with adaptive neighbors. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining, pp 977–986

  21. Meng Y, Shang R, Jiao L, Zhang W, Yuan Y, Yang S (2018) Feature selection based dual-graph sparse non-negative matrix factorization for local discriminative clustering. Neurocomputing 290:87–99

    Article  Google Scholar 

  22. Shang R, Meng Y, Wang W, Shang F, Jiao L (2019) Local discriminative based sparse subspace learning for feature selection. Pattern Recogn 92:219–230

    Article  Google Scholar 

  23. Shang R, Meng Y, Liu C, Jiao L, Esfahani AMG, Stokin R (2019) Unsupervised feature selection based on kernel fisher discriminant analysis and regression learning. Mach Learn 290:659–686

    Article  MathSciNet  Google Scholar 

  24. Meng Y, Shang R, Shang F, Jiao L, Yang S, Stolkin R (2020) Semi-supervised graph regularized deep NMF with bi-orthogonal constraints for data representation. IEEE Trans Neural Netw Learn Syst 31(9):3245–3258

    Article  MathSciNet  Google Scholar 

  25. Zhu X, Li X, Zhang S, Ju C, Wu X (2017) Robust joint graph sparse coding for unsupervised spectral feature selection. IEEE Trans Neural Netw Learn Syst 28(6):1263–1275

    Article  MathSciNet  Google Scholar 

  26. Zhu X, Zhang S, Hu R, Zhu R, Song J (2018) Local and global structure preservation for robust unsupervised spectral feature selection. IEEE Trans Knowl Data Eng 30(3):517–529

    Article  Google Scholar 

  27. Wright J, Ganesh A, Rao S, Peng Y, Ma Y (2009) Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. In: Proceedings of advances in neural information processing systems (NIPS), pp 2080–2088

  28. 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 

  29. Chen J, Mao H, Sang Y, Yi Z (2017) Subspace clustering using a symmetric low-rank representation. Knowl-Based Syst 127:46–57

    Article  Google Scholar 

  30. Wang J, Wang X, Tian F, Liu C, Yu H (2017) Constrained low-rank representation for robust subspace clustering. IEEE Trans Cybern 47(12):4534–4546

    Article  Google Scholar 

  31. Wong W, Lai Z, Wen J, Fang X, Lu Y (2017) Low rank embedding for robust image feature extraction. IEEE Trans Image Process 26(6):2905–2917

    Article  MathSciNet  Google Scholar 

  32. Zhang Y, Xiang M, Yang B (2017) Low-rank preserving embedding. Pattern Recogn 70:112–125

    Article  Google Scholar 

  33. Chen Y, Lai Z, Wong WK, Shen L, Hu Q (2018) Low-rank linear embedding for image recognition. IEEE Trans Multimed 20(12):3212–3222

    Article  Google Scholar 

  34. Lu Y, Lai Z, Xu Y, Li X, Zhang D, Yuan C (2016) Low-rank preserving projections. IEEE Trans Cybern 46(8):1900–1913

    Article  Google Scholar 

  35. Li S, Fu Y (2016) Learning robust and discriminative subspace with low-rank constraints. IEEE Trans Neural Netw Learn Syst 27(11):2160–2173

    Article  MathSciNet  Google Scholar 

  36. Ding Z, Suh S, Han J, Choi C, Fu Y (2015) Discriminative low-rank metric learning for face recognition. In: Proceedings of 11th IEEE international conference and workshops on automatic face and gesture recognition (FG), pp 1–6

  37. Lu Y, Yuan C, Lai Z, Li X, Zhang D (2017) Nuclear norm-based 2DLPP for image classification. IEEE Trans Multimed 19(11):2391–2403

    Article  Google Scholar 

  38. Xie L, Yin M, Yin X, Liu Y, Yin G (2018) Low-rank sparse preserving projections for dimensionality reduction. IEEE Trans Image Process 27(11):5261–5274

    Article  MathSciNet  Google Scholar 

  39. Han N, Wu J, Liang Y, Fang X, Wong W, Teng S (2018) Low-rank and sparse embedding for dimensionality reduction. Neural Netw 108:202–216

    Article  Google Scholar 

  40. Zhu X, Zhang S, Li Y, Zhang J, Yang L, Fang Y (2019) Low-rank sparse subspace for spectral clustering. IEEE Trans Knowl Data Eng 31(8):1532–1543

    Article  Google Scholar 

  41. Lin Z, Chen M, Wu L, Ma Y (2009) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. Technical report, UIUC Technical Report UILU-ENG-09-2215

  42. Cai J, Candés EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982

    Article  MathSciNet  Google Scholar 

  43. Nie F, Huang H, Cai X, Ding C (2010) Efficient and robust feature selection via joint \({\ell }_{2,1}\)-norms minimization. In: Advances in neural information processing systems, pp 1813–1821

  44. Nie F, Wang X, Jordan MI, Huang H (2016) The constrained laplacian rank algorithm for graph-based clustering. In: The 30th AAAI conference on artificial intelligence (AAAI)

  45. Samaria FS, Harter AC (1994) Parameterisation of a stochastic model for human face identification. In: Proceedings of the 2nd IEEE workshop on applications of computer vision. IEEE, pp 138–142

  46. Sim T, Baker S, Bsat M (2010) The CMU pose, illumination, and expression database. IEEE Trans Pattern Anal Mach Intell 25(12):1615–1618

    Google Scholar 

  47. Georghiades AS, Belhumeur PN, Kriegman DJ (2001) From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 23(6):643–660

    Article  Google Scholar 

  48. Huang GB, Ramesh R, Berg T, Learned-Miller E (2007) Labeled faces in the wild: a database for studying face recognition in unconstrained environments. Technical report, Dept. Comput. Sci., Univ. Massachusetts, Amherst, MA, USA

Download references

Acknowledgements

This work is supported in part by the NSFC-Henan Talent Jointly Training Foundation of China (No. U1504621) and the Key Science Research Project of Higher Education in Henan Province of China (No. 18A120001).

Author information

Authors and Affiliations

  1. School of Computer and Information Engineering, Henan University, Kaifeng, China

    Haishun Du & Fan Zhang

  2. Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng, China

    Yuxi Wang & Yi Zhou

Authors
  1. Haishun Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuxi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yi Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haishun Du.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, H., Wang, Y., Zhang, F. et al. Low-Rank Discriminative Adaptive Graph Preserving Subspace Learning. Neural Process Lett 52, 2127–2149 (2020). https://doi.org/10.1007/s11063-020-10340-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-020-10340-6

Keywords

Search

Navigation