Fisher linear discriminant analysis (FLDA) is a classic linear feature extraction and dimensionality reduction approach for face recognition. It is known that geometric distribution weight information of image data plays an important role in machine learning approaches. However, FLDA does not employ the geometric distribution weight information of facial images in the training stage. Hence, its recognition accuracy will be affected. In order to enhance the classification power of FLDA method, this paper utilizes radial basis function (RBF) with fractional order to model the geometric distribution weight information of the training samples and proposes a novel geometric distribution weight information based Fisher discriminant criterion. Subsequently, a geometric distribution weight information based LDA (GLDA) algorithm is developed and successfully applied to face recognition. Two publicly available face databases, namely, ORL and FERET databases, are selected for evaluation. Compared with some LDA-based algorithms, experimental results exhibit that our GLDA approach gives superior performance. 1. Introduction Over the past two decades, face recognition (FR) has made great progress with the increasing computational power of computers and has become one of the most important biometric-based authentication technologies. The key issue of FR algorithm is dimensionality reduction for facial feature extraction. According to different processes of facial feature extraction, face recognition algorithms can be generally divided into two classes, namely, (local) geometric feature based and (holistic) appearance based [1]. The geometric feature-based approach is based on the shape and the location of facial components (such as eyes, eyebrows, nose, and mouth), which are extracted to represent a face geometric feature vector. However, for the appearance-based approach, it depends on the global facial pixel features, which are exploited to form a whole facial feature vector for face classification. Principle component analysis (PCA) [2] and linear discriminant analysis (LDA) [3] are two famous appearance-based approaches for linear feature extraction and dimensionality reduction. They are also called Eigenface method and Fisherface method in face recognition, respectively. The objective of PCA is to find the orthogonal principle component (PC) directions and preserve the maximum variance information of the training data along PC directions. PCA can reconstruct each facial image using all Eigenfaces. Since PCA takes no account of the discriminant information, it is
References
[1]
R. Brunelli and T. Poggio, “Face recognition: features versus templates,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 10, pp. 1042–1052, 1993.
[2]
M. A. Turk and A. P. Pentland, “Face recognition using eigenfaces,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 586–591, June 1991.
[3]
P. N. Belhumeur, J. P. Hespanha, and D. J. Kriegman, “Eigenfaces vs. fisherfaces: recognition using class specific linear projection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711–720, 1997.
[4]
A. M. Martinez and A. C. Kak, “PCA versus LDA,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 2, pp. 228–233, 2001.
[5]
L.-F. Chen, H.-Y. M. Liao, M.-T. Ko, J.-C. Lin, and G.-J. Yu, “New LDA-based face recognition system which can solve the small sample size problem,” Pattern Recognition, vol. 33, no. 10, pp. 1713–1726, 2000.
[6]
H. Yu and J. Yang, “A direct LDA algorithm for high-dimensional data-with application to face recognition,” Pattern Recognition, vol. 34, no. 10, pp. 2067–2070, 2001.
[7]
W.-S. Chen, P. C. Yuen, and J. Huang, “A new regularized linear discriminant analysis method to solve small sample size problems,” International Journal of Pattern Recognition and Artificial Intelligence, vol. 19, no. 7, pp. 917–935, 2005.
[8]
P. Howland, J. Wang, and H. Park, “Solving the small sample size problem in face recognition using generalized discriminant analysis,” Pattern Recognition, vol. 39, no. 2, pp. 277–287, 2006.
[9]
W. S. Chen, P. C. Yuen, J. Huang, and B. Fang, “Two-step single parameter regularization fisher discriminant method for face recognition,” International Journal of Pattern Recognition and Artificial Intelligence, vol. 20, no. 2, pp. 189–208, 2006.
[10]
J. D. Tebbens and P. Schlesinger, “Improving implementation of linear discriminant analysis for the high dimension/small sample size problem,” Computational Statistics & Data Analysis, vol. 52, no. 1, pp. 423–437, 2007.
[11]
K. Das and Z. Nenadic, “An efficient discriminant-based solution for small sample size problem,” Pattern Recognition, vol. 42, no. 5, pp. 857–866, 2009.
[12]
H. Hu, P. Zhang, and F. De la Torre, “Face recognition using enhanced linear discriminant analysis,” IET Computer Vision, vol. 4, no. 3, pp. 195–208, 2010.
[13]
D. Chu and G. S. Thye, “A new and fast implementation for null space based linear discriminant analysis,” Pattern Recognition, vol. 43, no. 4, pp. 1373–1379, 2010.
[14]
W.-S. Chen, P. C. Yuen, and X. Xie, “Kernel machine-based rank-lifting regularized discriminant analysis method for face recognition,” Neurocomputing, vol. 74, no. 17, pp. 2953–2960, 2011.
[15]
A. Sharma and K. K. Paliwal, “A two-stage linear discriminant analysis for face-recognition,” Pattern Recognition Letters, vol. 33, no. 9, pp. 1157–1162, 2012.
[16]
F. Dornaika and A. Bosaghzadeh, “Exponential local discriminant embedding and its application to face recognition,” IEEE Transactions on Cybernetics, vol. 43, no. 3, pp. 921–934, 2013.
[17]
K. Fukunaga, Introduction to Statistical Pattern Recognition, Computer Science and Scientific Computing, Academic Press, Boston, Mass, USA, 2nd edition, 1990.
[18]
C. Liu, “Gabor-based kernel PCA with fractional power polynomial models for face recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 572–581, 2004.
[19]
C. Cattani and A. Ciancio, “Separable transition density in the hybrid model for tumor-immune system competition,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 610124, 6 pages, 2012.
[20]
C. Cattani, A. Ciancio, and B. Lods, “On a mathematical model of immune competition,” Applied Mathematics Letters, vol. 19, no. 7, pp. 678–683, 2006.
[21]
M. Li and W. Zhao, “Representation of a stochastic traffic bound,” IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 9, pp. 1368–1372, 2010.
[22]
M. Li, “Approximating ideal filters by systems of fractional order,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 365054, 6 pages, 2012.
[23]
M. Li, W. Zhao, and C. Cattani, “Delay bound: fractal traffic passes through servers,” Mathematical Problems in Engineering. In press.
[24]
S. X. Hu, Z. W. Liao, and W. F. Chen, “Sinogram restoration for low-dosed X-ray computed tomography using fractional-order perona-Malik Diffusion,” Mathematical Problems in Engineering, vol. 2012, Article ID 391050, 13 pages, 2012.
[25]
S. X. Hu, “External fractional-order gradient vector Perona-Malik Diffusion for sinogram restoration of low-dosed X-ray computed tomography,” Advances in Mathematical Physics, vol. 2013, Article ID 516919, 14 pages, 2013.
[26]
P. J. Phillips, H. Moon, S. A. Rizvi, and P. J. Rauss, “The FERET evaluation methodology for face-recognition algorithms,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1090–1104, 2000.
