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Two-dimensional locality adaptive discriminant analysis

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Abstract

Two-dimensional Linear Discriminant Analysis (2DLDA), which is supervised and extracts the most discriminating features, has been widely used in face image representation and recognition. However, 2DLDA is inapplicable to many real-world situations because it assumes that the input data obeys the Gaussian distribution and emphasizes the global relationship of data merely. To handle this problem, we present a Two-dimensional Locality Adaptive Discriminant Analysis (2DLADA). Compared to 2DLDA, our method has two salient advantages: (1) it does not depend on any assumptions on the data distribution and is more suitable in real world applications; (2) it adaptively exploits the intrinsic local structure of data manifold. Performance on artificial dataset and real-world datasets demonstrate the superiority of our proposed method.

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References

  1. Abou-Moustafa KT, Torre FDL, Ferrie FP (2015) Pareto models for discriminative multiclass linear dimensionality reduction. Pattern Recogn 48(5):1863–1877

    Article  Google Scholar 

  2. Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Bian W, Tao D (2011) Max-min distance analysis by using sequential sdp relaxation for dimension reduction. IEEE Trans Pattern Anal Mach Intell 33(5):1037–1050

    Article  Google Scholar 

  5. Ding C, Zhou D, He X, Zha H (2006) R1-pca:rotational invariant l1-norm principal component analysis for robust subspace factorization. In: International conference on machine learning, pp 281–288

  6. Friedman JH (1989) Regularized discriminant analysis. J Am Stat Assoc 84(405):165–175

    Article  MathSciNet  Google Scholar 

  7. Gao Q, Liu J, Zhang H, Hou J, Yang X (2012) Enhanced fisher discriminant criterion for image recognition. Pattern Recogn 45(10):3717–3724

    Article  Google Scholar 

  8. Gao Q, Gao F, Zhang H, Hao X, Wang X (2013) Two-dimensional maximum local variation based on image euclidean distance for face recognition. IEEE Trans Image Process 22(10):3807–3817

    Article  MathSciNet  Google Scholar 

  9. Gao Q, Ma L, Liu Y, Gao X, Nie F (2018) Angle 2dpca: a new formulation for 2dpca. IEEE Trans Cybern 48(5):1672–1678

    Article  Google Scholar 

  10. Gao Q, Xu S, Chen F, Ding C, Gao X, Li Y (2018) R1-2dpca and face recognition. IEEE Trans Cybern PP(99):1–7. https://doi.org/10.1109/TCYB.2018.2796642

    Article  Google Scholar 

  11. 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 

  12. Ghassabeh YA, Rudzicz F, Moghaddam HA (2015) Fast incremental lda feature extraction. Pattern Recogn 48(6):1999–2012

    Article  Google Scholar 

  13. Gu Z, Shao M, Li L, Fu Y (2013) Discriminative metric: Schatten norm vs. vector norm. In: International conference on pattern recognition, pp 1213–1216

  14. Hull JJ (2002) A database for handwritten text recognition research. IEEE Trans Pattern Anal Mach Intell 16(5):550–554

    Article  Google Scholar 

  15. Ke Q, Kanade T (2005) Robust l1 norm factorization in the presence of outliers and missing data by alternative convex programming. In: Proceedings of IEEE conference on computer vision and pattern recognition, pp 739–746

  16. Li H, 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 

  17. Li X, Pang Y, Yuan Y (2010) L1-norm-based 2dpca. IEEE Trans Syst Man Cybern B 40(4):1170–1175

    Article  Google Scholar 

  18. Li C, Shao Y, Deng N (2015) Robust l1-norm two-dimensional linear discriminant analysis. Neural Netw 65(C):92–104

    Article  Google Scholar 

  19. Li BN, Yu Q, Wang R, Xiang K, Wang M, Li X (2017) Block principal component analysis with nongreedy ℓ1-norm maximization. IEEE Trans Cybern 46(11):2543–2547

  20. Li M, Wang J, Wang Q, Gao Q (2017) Trace ratio 2dlda with l1-norm optimization. Neurocomputing 266:216–225

    Article  Google Scholar 

  21. Li X, Chen M, Nie F, Wang Q (2017) Locality adaptive discriminant analysis. In: Twenty-sixth international joint conference on artificial intelligence, pp 2201–2207

  22. Liu Y, Gao Q, Miao S, Gao X, Nie F, Li Y (2016) A non-greedy algorithm for l1-norm lda. IEEE Trans Image Process 26(2):684–695

    Article  MathSciNet  Google Scholar 

  23. Lu M, Huang JZ, Qian X (2016) Sparse exponential family principal component analysis. Pattern Recogn 60:681–691

    Article  Google Scholar 

  24. Martinez AM (1998) The ar face database. Cvc Technical Report 24

  25. Nie F, Xiang S, Zhang C (2007) Neighborhood minmax projections. In: International joint conference on artifical intelligence, pp 993–998

  26. Oh J, Kwak N (2016) Generalized mean for robust principal component analysis. Pattern Recogn 54(6):116–127

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Shao G, Sang N (2017) Regularized max-min linear discriminant analysis. Pattern Recogn 66:353–363

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Wang H, Nie F, Huang H (2014) Robust distance metric learning via simultaneous l1-norm minimization and maximization. In: International conference on machine learning, pp 1836–1844

  32. Wang S, Lu J, Gu X, Du H, Yang J (2016) Semi-supervised linear discriminant analysis for dimension reduction and classification. Pattern Recogn 57(C):179–189

    Article  Google Scholar 

  33. Wang H, Lu X, Hu Z, Zheng W (2017) Fisher discriminant analysis with l1-norm. IEEE Trans Cybern 44(6):828–842

  34. Wang Q, Gao Q, Gao X, Nie F (2018) L2p-norm based pca for image recognition. IEEE Trans Image Process 27(3):1336–1346

    Article  MathSciNet  Google Scholar 

  35. Wang Q, Gao Q, Xie D, Gao X, Yong W (2018) Robust dlpp with nongreedy ℓ1-norm minimization and maximization. IEEE Trans Neural Netw Learn Syst 29(3):738–743

  36. Yang J, Yang J, Frangi AF, Zhang D (2003) Uncorrelated projection discriminant analysis and its application to face image feature extraction. Int J Pattern Recognit Artif Intell 17(08):1325–1347

    Article  Google Scholar 

  37. Yang J, Zhang D, Frangi AF, Yang JY (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 

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

    Article  Google Scholar 

  39. Ye H, Li Y, Chen C, Zhang Z (2017) Fast fisher discriminant analysis with randomized algorithms. Pattern Recogn 72:82–92

    Article  Google Scholar 

  40. 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 

Download references

Acknowledgments

This work is supported by the Collaborative Innovation Platform of shenzhen institute of information technology, theShenzhen Fundamental Research fund under Grant JCYJ20160530141902978, the National Natural Science Foundation of China under Grant 61773302, and the Natural Science Foundation of Ningbo: 2018A610049. We thank Yinfeng Wang and Xiaojun Yang for their language editing, thank Deyan Xie for her writing assistance.

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Correspondence to Qin Li.

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Li, Q., You, J. Two-dimensional locality adaptive discriminant analysis. Multimed Tools Appl 78, 30397–30418 (2019). https://doi.org/10.1007/s11042-019-07861-1

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