Abstract
This paper develops a supervised discriminant technique, called graph embedding discriminant analysis (GEDA), for dimensionality reduction of high-dimensional data in small sample size problems. GEDA can be seen as a linear approximation of a multimanifold-based learning framework in which nonlocal property is taken into account besides the marginal property and local property. GEDA seeks to find a set of perfect projections that not only can impact the samples of intraclass and maximize the margin of interclass, but also can maximize the nonlocal scatter at the same time. This characteristic makes GEDA more intuitive and more powerful than linear discriminant analysis (LDA) and marginal fisher analysis (MFA). The proposed method is applied to face recognition and is examined on the Yale, ORL and AR face image databases. The experimental results show that GEDA consistently outperforms LDA and MFA when the training sample size per class is small.
Similar content being viewed by others
References
Jain AK, Duin RPW, Mao J (2000) Statistical pattern recognition: a review. IEEE Trans Pattern Anal Mach Int 22(1):4–37
Joliffe I (1986) Principal component analysis. Springer, Berlin
Fukunnaga K (1991) Introduction to statistical pattern recognition, 2nd edn. Academic Press, New York
Martinez AM, Kak AC (2001) PCA versus LDA. IEEE Trans Pattern Anal Mach Int 23(2):228–233
He X, Niyogi P (2003) Locality preserving projections. In: Proceedings of 16th conference neural information processing systems
Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323
Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323–2326
Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396
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 Int 40–51
Yang J, Zhang D, Yang JY, Niu B (2007) Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics. IEEE Trans Pattern Anal Mach Int 29(4):650–664
F. Chung (1997) Spectral Graph Theory. Reg Conf Ser Math no. 92
Golub GH, VanLoan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, US
Wan MH, Lai ZH, Shao J, Jin Z (2009) Two-dimensional local graph embedding discriminant analysis (2DLGEDA) with its application to face and palm biometrics. Neurocomputing 73:193–203
Yang WK, Wang JG, Ren MW, Yang JY (2009) Feature extraction based on laplacian bidirectional maximum margin criterion. Pattern Recogn 42(11):2327–2334
Zhao CR, Liu CC, Lai ZH (2011) Multi-scale gist feature manifold for building recognition. Neurocomputing 74(17):2929–2940
Zhao CR, Lai ZH, Liu CC, Gu XJ, Qian JJ (2012) Fuzzy local maximal marginal embedding for feature extraction. Soft Comput 16(1):77–87
Miao DQ, Gao C, Zhang N, Zhang ZF (2011) Diverse reduct subspaces based co-training for partially labeled data. Int J Approx Reason 52(8):1103–1117
Yang WK, Sun CY, Zhang L (2011) A multi-manifold discriminant analysis method for image feature extraction. Pattern Recogn 44(8):1649–1657
Lai ZH, Wong WK, Jin Z, Yang J, Xu Y (2012) Sparse approximation to the eigensubspace for discrimination. IEEE Trans Neural Netw Learn Syst 23(12):1948–1960
Wan MH (2012) Maximum inter-class and marginal discriminant embedding (MIMDE) for feature extraction and classification. Neural Comput Appl 21(7):1737–1743
Wan MH, Yang GW, Jin Z (2011) Feature extraction based on Fuzzy local discriminant embedding (FLDE) with applications to face recognition. IET Comput Vision 5(5):301–308
Acknowledgments
The authors would like to thank the anonymous reviewers for their critical and constructive comments and suggestions. This work is partially supported by China Postdoctoral Science Foundation under grant No. 2011M500626, 2012M511479 and China National Natural Science Foundation under grant No. 61203247, 61273304, 61203376, 61202170, 61103067 and 61075056. It is also partially supported by The Project Supported by Fujian and Guangdong Natural Science Foundation under grant No. 2012J01281 and S2012040007289, respectively. It is also partially supported by the Fundamental Research Funds for the Central Universities.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Cairong Zhao and Zhihui Lai contributed equally to this work.
Rights and permissions
About this article
Cite this article
Zhao, C., Lai, Z., Miao, D. et al. Graph embedding discriminant analysis for face recognition. Neural Comput & Applic 24, 1697–1706 (2014). https://doi.org/10.1007/s00521-013-1403-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-013-1403-1