Abstract：Neighborhood preserving embedding directly reconstructs the sample by its K-nearest neighbors. However, it does not distinguish the importance between intra-class neighbors and inter-class neighbors, which leads to poor recognition performance. In this paper, a common vector-based fuzzy neighborhood preserving embedding (FNPE/CV) algorithm is proposed.Firstly, the degree of membership of every sample for each class is obtained based on the class labels of its K-nearest neighbors. Then, every sample is reconstructed by the common vector and its membership grade for every class. Finally, the problem of minimizing the residual between original sample and its reconstruction sample is converted to solve the generalized eigenvalue problem to obtain the final projection transformation matrix. After the projecting, FNPE/CV minimizes the difference among intra-class samples and separates inter-class samples as far as possible. The experiments on ORL, Yale, AR and PIEC29 face databases demonstrate the effectiveness of the proposed algorithm.
[1] Turk M A, Pentland A P. Eigenface for recognition. Jorunal of Cognitive Neuroscience, 1991, 3 (1): 71-86 [2] Belhumeur P N, Hespanha J P, Kriegman D J. Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection. IEEE Trans on Pattern Analysis and Machine Intelligence, 1997, 19 (7): 711-720 [3] Belkin M, Niyogi P. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation, 2003, 15(6): 1373-1396 [4] Roweis S T, Saul L K. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science, 2000, 290(5500): 2323-2326 [5] He X F, Niyogi P. Locality Preserving Projections // Proc of the Conference on Advances in Neural Information Processing Systems 16. Vancouver, Canada, 2003: 153-160 [6] He X F, Cai D, Yan S C, et al. Neighborhood Preserving Embedding // Proc of the 10th IEEE International Conference on Computer Vision. Beijing, China, 2005, II: 1208-1213 [7] Bilginer G B, Dzhafarov V, Keskin M, et al. A Novel Approach to Isolated Word Recognition. IEEE Trans on Speech and Audio Processing, 1999, 7(6): 620-628 [8] Gülmezoglu M B, Dzhafarov V, Barkana A. The Common Vector Approach and Its Relation to Principal Component Analysis. IEEE Trans on Speech and Audio Processing, 2001, 9(6): 655-662 [9] Cevikalp H, Neamtu M, Wilkes M, et al. Discriminative Common Vectors for Face Recognition. IEEE Trans on Pattern Analysis and Machine Intelligence, 2005, 27(1): 4-13 [10] He Y H, Zhao L, Zou C R. Kernel Discriminative Common Vectors for Face Recognition // Proc of the International Conference on Machine Learning and Cybernetics. Guangzhou, China, 2005, VIII: 4605-4610 [11] He Y H, Zhao L, Zou C R. Face Recognition Using Common Faces Method. Pattern Recognition, 2006, 39(11): 2218-2222 [12] Wen Y, He L H, Shi P F. Face Recognition Using Difference Vector Plus KPCA. Digital Signal Processing, 2012, 22(1): 140-146 [13] Wen Y, Shi P F. An Approach to Face Recognition Based on Common Vector and 2DPCA. Acta Automatica Sinica, 2009, 35(2): 202-205 (in Chinese) (文 颖,施鹏飞.一种基于共同向量结合2DPCA的人脸识别方法.自动化学报, 2009, 35(2): 202-205) [14] Li R D, Zhu L, Yu D H, et al. Making Discriminative Common Vectors Applicable to Face Recognition with One Training Image per Person. Journal of Zhejiang University: Science Edition, 2008, 35(2): 181-184 (in Chinese) (李瑞东,祝 磊,余党军,等.基于判别公共向量的单训练样本人脸识别.浙江大学学报:理学版, 2008, 35(2): 181-184) [15] Keller J M, Gray M R, Givens J A. A Fuzzy K-nearest Neighbor Algorithm. IEEE Trans on Systems, Man and Cybernetics, 1985, SMC-15(4): 580-585 [16] Khoukhi A, Ahmed S F. A Genetically Modified Fuzzy Linear Discriminant Analysis for Face Recognition. Journal of the Franklin Institute, 2011, 348(10): 2701-2717
2014, Vol. 27 
