Manifold learning algorithms mainly focus on discovering the intrinsic low-dimensional manifold embedded in the high-dimensional Euclidean space. Among them, locally linear embedding (LLE) is one of the most promising dimensionality reduction methods. Though LLE holds local neighborhood information, it doesn’t fully take the label information and the global structure information into account for classification tasks. To enhance classification performance, this paper proposes a novel dimensionality reduction method for face recognition, termed embedded manifold-based kernel Fisher discriminant analysis, or EMKFDA for short. The goal of EMKFDA is to emphasize the local geometry structure of the data while utilizing the global discriminative structure obtained from linear discriminant analysis, which can maximize the between-class scatter and minimize the within-class scatter. In addition, by optimizing an objective function in a kernel feature space, nonlinear features can be extracted. Thus, EMKFDA, which combines manifold criterion and Fisher criterion, has better discrimination, and is more suitable for recognition tasks. Experiments on the ORL, Yale, and FERET face databases show the impressive performance of the proposed method. Results show that this proposed algorithm exceeds other popular approaches reported in the literature and achieves much higher recognition accuracy.
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Zhao W, Chellappa R, Phillips PJ, Rosenfeld A (2003) Face recognition: a literature survey. ACM Comput Surv 35(4):399–458
Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86
Belhumeour PN, Hedpsnhs JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720
Howland P, Wang JL, Park H (2006) Solving the small sample size problem in face recognition using generalized discriminant analysis. Pattern Recognit 39(2):277–287
Liang YX, Li CR, Gong WG, Pan YJ (2007) Uncorrelated linear discriminant analysis based on weighted pairwise Fisher criterion. Pattern Recognit 40(12):3606–3625
Zhao W, Zhao L, Zou C (2004) An efficient algorithm to solve the small sample size problem for LDA. Pattern Recognit 37(5):1077–1079
Ye J, Li Q (2005) A two-stage linear discriminant analysis via QR-decomposition. IEEE Trans Pattern Anal Mach Intell 27(6):929–941
Scholkopf B, Smola A, Muller KR (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10(5):1299–1319
Baudat G, Anouar F (2000) Generalized discriminant analysis using a kernel approach. Neural Comput 12(10):2385–2404
Tenebaum J, Silva V, Langford J (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 (2001) Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Proceedings of neural information processing systems, Vancouver, pp 585–591
Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396
Weinberger K, Saul L (2004) Unsupervised learning of image manifolds by semidefinite programming. In: Proceedings of the IEEE international conference computer vision and pattern recognition, vol 2, pp 988–985
Zhang Z, Zha H (2005) Principal manifolds and nonlinear dimensionality reduction via local tangent space alignment. SIAM J Sci Comput 26(1):313–318
Zhang TH, Li XL, Tao DC, Yang J (2008) Local coordinates alignment (LCA): a novel method for manifold learning. Int J Pattern Recognit Artif Intell 22(4):667–690
Xiang SM, Nie FP, Xiang SM, Zhuang YT, Wang WH (2009) Nonlinear dimensionality reduction with local spline embedding. IEEE Trans Knowl Data Eng 21(9):1285–1298
He X, Cai D, Yan S, Zhang H (2005) Neighborhood preserving embedding. In: Proceedings of the IEEE international conference computer vision, pp 1208–1213
He X, Yan S, Hu Y, Niyogi P, Zhang HJ (2005) Face recognition using Laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340
Chen HT, Chang HW, Liu TL (2005) Local discriminant embedding and its variants. In: Proceedings of the conference on computer vision and pattern recognition, vol 2, pp 846–853
Yan SC, Xu D, Zhang BY, Zhang HJ (2005) Graph embedding: a general framework for dimensionality reduction. In: Proceedings of the conference on computer vision and pattern recognition, vol 2, pp 20–25
Cai D, He XF, Zhou K (2007) Locality sensitive discriminant analysis. In: Proceedings of the conference on artificial intelligence, pp 708–713
Vapnik V (1995) The nature of statistical learning theory. Springer, New York
The ORL face database. http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html. Accessed 2004
The Yale face database. http://cvc.yale.edu/projects/yalefaces/yalefaces.html. Accessed 2004
Seung HS, Lee DD (2000) The manifold ways of perception. Science 290:2258–2259
Zhang J, Li SZ, Wang J (2004) Manifold learning and applications in recognition. In: Intelligent multimedia processing with soft computing, vol 168, pp 281–300
Li B, Huang DS (2008) Locally linear discriminant embedding: an efficient method for face recognition. Pattern Recognit 41(12):3813–3821
Pang YW, Yu NH, Li HQ et al (2005) Face recognition using neighborhood preserving projections. In: Proceedings of pacific-rim conference on multimedia, vol 3768, pp 854–864
Li H, Jiang T, Zhang K (2006) Efficient and robust feature extraction by maximum margin criterion. IEEE Trans Neural Netw 17(1):157–165
Saul LK, Roweis ST (2003) Think globally, fit locally: unsupervised learning of low dimensional manifolds. J Mach Learn Res 4:119–155
The facial recognition technology (FERET) database. http://www.itl.nist.gov/iad/humanid/feret/feret_master.html. Accessed 2008
Zhang TH, Tao DC, Li XL, Yang J (2008) A unifying framework for spectral analysis based dimensionality reduction. In: Proceedings of the international joint conference on neural networks, pp 1670–1677
This work is supported by the Young Core Instructor of Colleges and Universities in Henan Province Funding Scheme (No. 2011GGJS-173), the Science and Technology Project of Henan Province (No. 122102210138), Foundation of Henan Educational Committee (No. 14A520055), the Nation Scholarship Fund (No. 201308410352).
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Wang, G., Shi, N., Shu, Y. et al. Embedded Manifold-Based Kernel Fisher Discriminant Analysis for Face Recognition. Neural Process Lett 43, 1–16 (2016). https://doi.org/10.1007/s11063-014-9398-x
- Face recognition
- Dimensionality reduction
- Manifold learning
- Locally linear embedding
- Kernel discriminant analysis