Advertisement

Multimedia Tools and Applications

, Volume 77, Issue 3, pp 3071–3081 | Cite as

Stable and orthogonal local discriminant embedding using trace ratio criterion for dimensionality reduction

  • Xiaojun Yang
  • Gang Liu
  • Qiang Yu
  • Rong Wang
Article

Abstract

Stable orthogonal local discriminant embedding (SOLDE) is a recently proposed dimensionality reduction method, in which the similarity, diversity and interclass separability of the data samples are well utilized to obtain a set of orthogonal projection vectors. By combining multiple features of data, it outperforms many prevalent dimensionality reduction methods. However, the orthogonal projection vectors are obtained by a step-by-step procedure, which makes it computationally expensive. By generalizing the objective function of the SOLDE to a trace ratio problem, we propose a stable and orthogonal local discriminant embedding using trace ratio criterion (SOLDE-TR) for dimensionality reduction. An iterative procedure is provided to solve the trace ratio problem, due to which the SOLDE-TR method is always faster than the SOLDE. The projection vectors of the SOLDE-TR will always converge to a global solution, and the performances are always better than that of the SOLDE. Experimental results on two public image databases demonstrate the effectiveness and advantages of the proposed method.

Keywords

Trace ratio criterion Manifold learning Dimensionality reduction Diversity 

Notes

Acknowledgements

This paper is supported by National Natural Science Foundation of China (No.61401471 and No.61501471); General Financial from the China Postdoctoral Science Foundation (No.2014M552589) and Special Financial from the China Postdoctoral Science Foundation (No.2015T81114).

References

  1. 1.
    Belhumeur P N, Hespanha J P, Kriegman D J (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720CrossRefGoogle Scholar
  2. 2.
    Benmokhtar R, Delhumeau J, Gosselin P H (2013) Efficient supervised dimensionality reduction for image categorization. In: Proceedings of the 2013 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 2425–2428Google Scholar
  3. 3.
    Boughnim N, Marot J, Fossati C, Bourennane S, Guerault F (2013) Fast and improved hand classification using dimensionality reduction and test set reduction. In: Proceedings of the 2013 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 1971–1975Google Scholar
  4. 4.
    Cai D, He X, Han J, Zhang H (2006) Orthogonal laplacianfaces for face recognition. IEEE Trans Image Process 15(11):3608–3614CrossRefGoogle Scholar
  5. 5.
    Cai D, He X, Zhou K, Han J, Bao H (2007) Locality sensitive discriminant analysis. In: Proceedings of the 20th international joint conference on artificial intelligence, pp 708–713Google Scholar
  6. 6.
    Chang X, Ma Z, Yang Y, Zeng Z, Hauptmann AG (2016) Bi-level semantic representation analysis for multimedia event detection. IEEE Trans Cybern 1–18. doi: 10.1109/TCYB.2016.2539546
  7. 7.
    Chang X, Nie F, Wang S, Yang Y, Zhou X, Zhang C (2016) Compound rank- k projections for bilinear analysis. IEEE Trans Neural Netw Learn Syst 27(7):1502–1513MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chang X, Yang Y (2016) Semisupervised feature analysis by mining correlations among multiple tasks. IEEE Trans Neural Netw Learn Syst 1–12. doi: 10.1109/TNNLS.2016.2582746
  9. 9.
    Chang X, Yang Y, Long G, Zhang C, Hauptmann A G (2016) Dynamic concept composition for zero-example event detection. In: AAAIGoogle Scholar
  10. 10.
    Chang X, Yu YL, Yang Y, Xing EP (2016) Semantic pooling for complex event analysis in untrimmed videos. IEEE Trans Pattern Anal Mach Intell (99). doi: 10.1109/TCYB.2015.2479645
  11. 11.
    Duchene J, Leclercq S (1988) An optimal transformation for discriminant and principal component analysis. IEEE Trans Pattern Anal Mach Intell 10(6):978–983CrossRefMATHGoogle Scholar
  12. 12.
    Gao Q, Ma J, Zhang H, Gao X, Liu Y (2013) Stable orthogonal local discriminant embedding for linear dimensionality reduction. IEEE Trans Image Process 22(7):2521–2531CrossRefGoogle Scholar
  13. 13.
    Guo Y F, Li S J, Yang J Y, Shu T T, Wu L D (2003) A generalized foley–sammon transform based on generalized fisher discriminant criterion and its application to face recognition. Pattern Recogn Lett 24(1):147–158CrossRefMATHGoogle Scholar
  14. 14.
    He X, Yan S, Hu Y, Niyogi P, Zhang H (2005) Face recognition using laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340CrossRefGoogle Scholar
  15. 15.
    Jia Y, Nie F, Zhang C (2009) Trace ratio problem revisited. IEEE Trans Neural Netw 20(4):729–735CrossRefGoogle Scholar
  16. 16.
    Li B N, Yu Q, Wang R, Xiang K, Wang M, Li X (2016) Block principal component analysis with nongreedy 1-norm maximization. IEEE Trans Cybern 46(11):2543–2547CrossRefGoogle Scholar
  17. 17.
    Li H, Jiang T, Zhang K (2006) Efficient and robust feature extraction by maximum margin criterion. IEEE Trans Neural Netw 17(1):157–165CrossRefGoogle Scholar
  18. 18.
    Luo M, Chang X, Nie L, Yang Y, Hauptmann AG, Zheng Q (2017) An adaptive semisupervised feature analysis for video semantic recognition. IEEE Trans Cybern. doi: 10.1109/TCYB.2017.2647904
  19. 19.
    Parisotto E, Ghassabeh Y A, Freydoonnejad S, Rudzicz F (2015) Eeg dimensionality reduction in automatic identification of synonymy. In: 2015 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 847–851Google Scholar
  20. 20.
    Wang H, Lu X, Hu Z, Zheng W (2014) Fisher discriminant analysis with L1-norm. IEEE Trans Cybern 44(6):828–842CrossRefGoogle Scholar
  21. 21.
    Wang H, Yan S, Xu D, Tang X, Huang T (2007) Trace ratio vs. ratio trace for dimensionality reduction. In: Proceedings of the 2007 IEEE conference on computer vision and pattern recognition, pp 1–8Google Scholar
  22. 22.
    Wang R, Nie F, Hong R, Chang X, Yang X, Yu W (2017) Fast and orthogonal locality preserving projections for dimensionality reduction. IEEE Trans Image Process PP(99):1–1. ISSN 1057-7149. doi: 10.1109/TIP.2017.2726188 MathSciNetGoogle Scholar
  23. 23.
    Wang S, Chen H, Peng X, Zhou C (2011) Exponential locality preserving projections for small sample size problem. Neurocomputing 74(17):3654–3662CrossRefGoogle Scholar
  24. 24.
    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):40–51CrossRefGoogle Scholar
  25. 25.
    Zhang T, Huang K, Li X, Yang J, Tao D (2010) Discriminative orthogonal neighborhood-preserving projections for classification. IEEE Trans Syst Man Cyberns Part B: Cybern 40(1):253–263CrossRefGoogle Scholar
  26. 26.
    Zoidi O, Nikolaidis N, Pitas I (2014) Semi-supervised dimensionality reduction on data with multiple representations for label propagation on facial images. In: Proceedings of the 2014 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 6019–6023Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.The Center for OPTical IMagery Analysis and Learning (OPTIMAL)Northwestern Polytechnical UniversityXi’anChina
  2. 2.The School of Information EngineeringGuangdong University of TechnologyGuangzhouChina
  3. 3.The Xi’an Research Institute of Hi-TechXi’anChina

Personalised recommendations