Robust discriminant analysis with adaptive locality preserving

Abstract

Conventional linear discriminant analysis methods commonly ignore the information loss and locality preserving, which greatly limits their performance. To address these issues, we propose a novel discriminant analysis method for feature extraction in this paper. Specially, the proposed method simultaneously exploits the local information and label information to guide the projection learning by constraining the margins of samples from the same class with an adaptively learned weighted matrix, which enables the method to obtain a more compact and discriminative projection. To catch as much discriminant information as possible, a variant of principle component analysis (PCA) term is further introduced to constrain the projection. Besides, to reduce the negative influence of noise and redundant features, a spares error term and a sparse projection constraint are simultaneously introduced to the framework, which enables the method to adaptively select those important features during feature extraction. Compared with the other methods, the proposed method simultaneously holds many good properties including discriminability, locality, data reconstruction, and feature selection in a framework, and is robust to noise. These good properties encourage the method to perform better than the other methods. Extensive experimental results conducted on face, object, scene, and noisy databases verify the effectiveness of the proposed in feature extraction.

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Notes

  1. 1.

    Available at http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php.

  2. 2.

    Available at http://www2.ece.ohio-state.edu/~aleix/ARdatabase.html.

  3. 3.

    Available at http://vision.ucsd.edu/~iskwak/ExtYaleDatabase/ExtYaleB.html.

  4. 4.

    Available at http://www.ri.cmu.edu/projects/project_418.html.

References

  1. 1.

    Lai Z, Wan M, Jin Z, Yang J (2011) Sparse two-dimensional local discriminant projections for feature extraction. Neurocomputing 74(4):629–637

    Article  Google Scholar 

  2. 2.

    Lai Z, Mo D, Wong WK, Xu Y, Miao D, Zhang D (2017) Robust discriminant regression for feature extraction. IEEE Trans Cybern 48:2472–2484

  3. 3.

    Liu Q, Lu X, He Z, Zhang C, Chen W-S (2017) Deep convolutional neural networks for thermal infrared object tracking. Knowl Based Syst 134:189–198

    Article  Google Scholar 

  4. 4.

    Sun F, Yao Y, Li X (2018) The heat and mass transfer characteristics of superheated steam coupled with non-condensing gases in horizontal wells with multi-point injection technique. Energy 143:995–1005

    Article  Google Scholar 

  5. 5.

    Luo G, Dong S, Wang K, Zuo W, Cao S, Zhang H (2017) Multi-views fusion cnn for left ventricular volumes estimation on cardiac mr images. IEEE Trans Biomed Eng 9:1924–1934

    Google Scholar 

  6. 6.

    Fei L, Lu G, Jia W, Teng S, Zhang D (2018) Feature extraction methods for palmprint recognition: a survey and evaluation. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2018.2795609

    Article  Google Scholar 

  7. 7.

    Fang X, Yong X, Li X, Lai Z, Teng S, Fei L (2017) Orthogonal self-guided similarity preserving projection for classification and clustering. Neural Netw 88:1–8

    Article  Google Scholar 

  8. 8.

    Lai Z, Xu Y, Yang J, Shen L, Zhang D (2016) Rotational invariant dimensionality reduction algorithms. IEEE Trans Cybern 47(11):3733–3746

    Article  Google Scholar 

  9. 9.

    Sun F, Yao Y, Chen M, Li X, Zhao L, Meng Y, Sun Z, Zhang T, Feng D (2017) Performance analysis of superheated steam injection for heavy oil recovery and modeling of wellbore heat efficiency. Energy 125:795–804

    Article  Google Scholar 

  10. 10.

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

    Article  Google Scholar 

  11. 11.

    Dong S, Luo G, Wang K, Cao S, Li Q, Zhang H (2018) A combined fully convolutional networks and deformable model for automatic left ventricle segmentation based on 3D echocardiography. BioMed Res Int 2018:5682365

    Google Scholar 

  12. 12.

    Li J, Zhang B, Lu G, Ren H, Zhang D (2018) Visual classification with multikernel shared Gaussian process latent variable model. IEEE Trans Cybern (99): 1–14

  13. 13.

    Lu Y, Lai Z, Li X, Wong WK, Yuan C, Zhang D (2018) Low-rank 2-D neighborhood preserving projection for enhanced robust image representation. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2018.2815559

    Article  Google Scholar 

  14. 14.

    Wen J, Lai Z, Zhan Y, Cui J (2016) The L2, 1-norm-based unsupervised optimal feature selection with applications to action recognition. Pattern Recogn 60:515–530

    MATH  Article  Google Scholar 

  15. 15.

    Lu Y, Yuan C, Li X, Lai Z, Zhang D, Shen L (2018) Structurally incoherent low-rank 2DLPP for image classification. IEEE Trans Circuits Syst Video Technol. https://doi.org/10.1109/TCSVT.2018.2849757

    Article  Google Scholar 

  16. 16.

    Zhang L, Han J, Deng S (2018) Unsupervised temporal feature learning based on sparse coding embedded BoAW. In: Proceedings of the INTERSPEECH, 3284–3288

  17. 17.

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

    Article  Google Scholar 

  18. 18.

    Li L, Liu S, Peng Y, Sun Z (2016) Overview of principal component analysis algorithm. Opt Int J Light Electron Opt 127(9):3935–3944

    Article  Google Scholar 

  19. 19.

    He X, Niyogi P (2004) Locality preserving projections. In: Proceedings of the advances in neural information processing systems, 153–160

  20. 20.

    He X, Cai D, Yan S, Zhang H-J (2005) Neighborhood preserving embedding [C]. In: Proceedings of the IEEE International Conference on Computer Vision, 1208–1213

  21. 21.

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

    MathSciNet  MATH  Article  Google Scholar 

  22. 22.

    Camps-Valls G, Marsheva TVB, Zhou D (2007) Semi-supervised graph-based hyperspectral image classification. IEEE Trans Geosci Remote Sens 45(10):3044–3054

    Article  Google Scholar 

  23. 23.

    Fang X, Yong X, Li X, Lai Z (2016) Robust semi-supervised subspace clustering via non-negative low-rank representation. IEEE Trans Cybern 46(8):1828–1838

    Article  Google Scholar 

  24. 24.

    Sun F, Yao Y, Li X, Yu P, Zhao L, Zhang Y (2017) A numerical approach for obtaining type curves of superheated multi-component thermal fluid flow in concentric dual-tubing wells. Int J Heat Mass Transf 111:41–53

    Article  Google Scholar 

  25. 25.

    Fei L, Xu Y, Fang X, Yang J (2017) Low rank representation with adaptive distance penalty for semi-supervised subspace classification. Pattern Recogn 67:252–262

    Article  Google Scholar 

  26. 26.

    Zhang Z, Xu Y, Shao L, Yang J (2017) Discriminative block-diagonal representation learning for image recognition. IEEE Trans Neural Netw Learn Syst 1:1–16

    Article  Google Scholar 

  27. 27.

    Fei L, Lu G, Jia W, Wen J, Zhang D (2018) Complete binary representation for 3-D palmprint recognition. IEEE Trans Instrum Meas 67(12):2761–2771

    Article  Google Scholar 

  28. 28.

    Li J, Zhang B, Lu G, Zhang D (2019) Generative multi-view and multi-feature learning for classification. Inf Fus 45:215–226

    Article  Google Scholar 

  29. 29.

    Zhang Z, Shao L, Xu Y, Liu L, Yang J (2018) Marginal representation learning with graph structure self-adaptation. IEEE Trans Neural Netw 29(10):4645–4659

    MathSciNet  Article  Google Scholar 

  30. 30.

    Li L, Peng Y, Qiu G, Sun Z, Liu S (2018) A survey of virtual sample generation technology for face recognition. Artif Intell Rev 50(1):1–20

    Article  Google Scholar 

  31. 31.

    Li J, Zhang B, Zhang D (2017) Shared autoencoder Gaussian process latent variable model for visual classification. IEEE Trans Neural Netw Learn Syst

  32. 32.

    Peng Y, Li L, Liu S, Li J, Wang X, Extended sparse representation-based classification method for face recognition [J]. Machine Vision and Applications 2018: 1–17

  33. 33.

    Izenman J (2013) Linear discriminant analysis, Springer, Berlin

    Google Scholar 

  34. 34.

    Ma Z, Wen J, Liu Q, Tuo G (2015) Near-infrared and visible light image fusion algorithm for face recognition. J Mod Opt 62(9):745–753

    Article  Google Scholar 

  35. 35.

    Lai Z, Xu Y, Yang J, Tang J, Zhang D (2013) Sparse tensor discriminant analysis. IEEE Trans Image Process 22(10):3904–3915

    MathSciNet  MATH  Article  Google Scholar 

  36. 36.

    Yang J, Zhang D, Yong X, Yang J-y (2005) Two-dimensional discriminant transform for face recognition. Pattern Recogn 38(7):1125–1129

    MATH  Article  Google Scholar 

  37. 37.

    Lu Y, Yuan C, Lai Z, Li X, Zhang D, Wong WK (2018) Horizontal and vertical nuclear norm-based 2DLDA for image representation. IEEE Trans Circuits Syst Video Technol. https://doi.org/10.1109/TCSVT.2018.2822761

    Article  Google Scholar 

  38. 38.

    Ye J, Janardan R, Li Q, Park H (2006) Feature reduction via generalized uncorrelated linear discriminant analysis. IEEE Trans Knowl Data Eng 18(10):1312–1322

    Article  Google Scholar 

  39. 39.

    Shi X, Yang Y, Guo Z, Lai Z (2014) Face recognition by sparse discriminant analysis via joint L 2,1 -norm minimization. Pattern Recogn 47(7):2447–2453

    Article  Google Scholar 

  40. 40.

    Li X, Hu W, Wang H, Zhang Z (2010) Linear discriminant analysis using rotational invariant L1 norm. Neurocomputing 73(13–15):2571–2579

    Article  Google Scholar 

  41. 41.

    Zheng W, Lin Z, Wang H (2014) L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction. IEEE Trans Neural Netw Learn Syst 25(4):793–805

    Article  Google Scholar 

  42. 42.

    Wang H, Lu X, Hu Z, Zheng W (2014) Fisher discriminant analysis with L1-norm. IEEE Trans Cybern 44(6):828–842

    Article  Google Scholar 

  43. 43.

    Clemmensen L, Hastie T, Witten D, Ersbøll B (2011) Sparse discriminant analysis. Technometrics 53(4):406–413

    MathSciNet  Article  Google Scholar 

  44. 44.

    Zhang X, Chu D, Tan RCE (2016) Sparse uncorrelated linear discriminant analysis for undersampled problems. IEEE Trans Neural Netw Learn Syst 27(7):1469–1485

    MathSciNet  Article  Google Scholar 

  45. 45.

    Zhou Y, Sun S (2016) Manifold partition discriminant analysis. IEEE Trans Cybern 47(4):830–840

    Article  Google Scholar 

  46. 46.

    Yan S, Xu D, Zhang B, Zhang H-J, 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 

  47. 47.

    Zhang T, Tao D, Yang J, (2008) Discriminative locality alignment. In: Proceedings of the European Conference on Computer Vision, Marseille, France, 725–738

  48. 48.

    Li X, Chen M, Nie F, Wang Q (2017) Locality adaptive discriminant analysis. In: Proceedings of the International Joint Conference on Artificial Intelligence, 2201–2207

  49. 49.

    Wen J, Xu Y, Li Z, Ma Z, Xu Y (2018) Inter-class sparsity based discriminative least square regression. Neural Netw 102:36–47

    Article  Google Scholar 

  50. 50.

    Ma X, Liu Q, Ou W, Zhou Q (2018) Visual object tracking via coefficients constrained exclusive group LASSO. Mach Vis Appl 29: 1–15

    Article  Google Scholar 

  51. 51.

    Zhong Z, Zhang B, Lu G, Zhao Y, Xu Y (2017) An adaptive background modeling method for foreground segmentation. IEEE Trans Intell Transp Syst 18(5):1109–1121

    Article  Google Scholar 

  52. 52.

    Zhang Z, Liu L, Shen F, Shen HT, Shao L (2018) Binary multi-view clustering. IEEE Trans Pattern Anal Mach Intell

  53. 53.

    Wen J, Fang X, Cui J, Fei L, Yan K, Chen Y, Xu Y (2018) Robust sparse linear discriminant analysis. IEEE Trans Circuits Syst Video Technol. https://doi.org/10.1109/TCSVT.2018.2799214

    Article  Google Scholar 

  54. 54.

    Zou H, Hastie T, Tibshirani R (2006) Sparse principal component analysis. J Comput Graphical Stat 15(2):265–286

    MathSciNet  Article  Google Scholar 

  55. 55.

    Xiang S, Nie F, Meng G, Pan C, Zhang C (2012) Discriminative least squares regression for multiclass classification and feature selection. IEEE Trans Neural Netw Learn Syst 23(11):1738–1754

    Article  Google Scholar 

  56. 56.

    Fang X, Yong X, Li X, Lai Z, Wong WK, Fang B (2018) Regularized label relaxation linear regression. IEEE Trans Neural Netw Learn Syst 29(4):1006–1018

    Article  Google Scholar 

  57. 57.

    Wen J, Zhang B, Xu Y, Yang J, Han N (2018) Adaptive weighted nonnegative low-rank representation. Pattern Recogn 81:326–340

    Article  Google Scholar 

  58. 58.

    Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends® Mach Learn 3(1):1–122

    MATH  Google Scholar 

  59. 59.

    Wen J, Fang X, Xu Y, Tian C, Fei L (2018) Low-rank representation with adaptive graph regularization. Neural Netw 108:83–96

    Article  Google Scholar 

  60. 60.

    Wen J, Zhang Z, Xu Y, Zhong Z (2018) Incomplete multi-view clustering via graph regularized matrix factorization. In: Proceedings of the European Conference on Computer Vision Workshop, Munich, Germany

  61. 61.

    Cand EJ, s X, Li Y, Ma, Wright J (2009) Robust principal component analysis?. J ACM 58(1):1–73

    MathSciNet  Google Scholar 

  62. 62.

    Wen J, Han N, Fang X, Fei L, Yan K, Zhan S (2018) Low-rank preserving projection via graph regularized reconstruction. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2018.2799862

    Article  Google Scholar 

  63. 63.

    Qiao Z, Zhou L, Huang JZ (2009) Sparse linear discriminant analysis with applications to high dimensional low sample size data. Iaeng Int J Appl Math 39(1):48–60

    MathSciNet  MATH  Google Scholar 

  64. 64.

    Baudat G, Anouar F (2000) Generalized discriminant analysis using a kernel approach. Neural Comput 12(10):2385–2404

    Article  Google Scholar 

  65. 65.

    Fan Z, Xu Y, Ni M, Fang X, Zhang D (2016) Individualized learning for improving kernel Fisher discriminant analysis. Pattern Recogn 58:100–109

    MATH  Article  Google Scholar 

  66. 66.

    A. SKN, Nene HMSA (1996) Columbia object image library (COIL-20). Technical Report CUCS-005-96 1–6

  67. 67.

    Georghiades S, 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 

  68. 68.

    Martinez M (1998) The AR face database. Cvc Technical Report, 24

  69. 69.

    Sim T, Baker S, Bsat M (2003) The CMU pose, illumination, and expression database. IEEE Trans Pattern Anal Mach Intell 25(12):1615–1618

    Article  Google Scholar 

  70. 70.

    Jiang Z, Lin Z, Davis LS (2013) Label consistent K-SVD: learning a discriminative dictionary for recognition. IEEE Trans Pattern Anal Mach Intell 35(11):2651–2664

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (nos. 61703112, 61773128), Guangdong Natural Science Foundation (nos. 2014A030308009) and Guangdong Science and Technology Planning Project (nos. 2016B030308001, 2013B091300009, 2014B090907010, 2015B010131014 and 2017B010125002).

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Correspondence to Shengli Xie.

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Sun, W., Xie, S. & Han, N. Robust discriminant analysis with adaptive locality preserving. Int. J. Mach. Learn. & Cyber. 10, 2791–2804 (2019). https://doi.org/10.1007/s13042-018-00903-4

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Keywords

  • Discriminant analysis
  • Feature extraction
  • Locality preserving
  • Data reconstruction