|
|
|
| Discriminant Analysis on Nonlinear Manifold Based on Local Linear Discriminant Merging |
| CHEN HuaJie, WEI Wei |
| College of Electrical Engineering, Zhejiang University, Hangzhou 310027 |
|
|
|
|
Abstract A local linear discriminant merging method is proposed and the discriminant analysis is carried out on nonlinear manifold. The local linear discriminants were constructed at the local regions obtained by using the Gabriel Graph, then merged to achieve the global nonlinear discriminant. Each local discriminant was assigned to the best weight coefficient in iterative manner by following the margin criterion. So the global nonlinear problem is decomposed into the local linear problem and the discriminant merging problem, which are relatively easy to conquer. The margin criterion based merging algorithm can solve the “sample size sample” problem and ensure that the performance of the global discriminant is independent of the distribution of sample data. The superiority of proposed algorithm is confirmed by experiments on synthesized data and face image set.
|
|
Received: 18 January 2006
|
|
|
|
|
|
[1] Roweis S T, Saul L K. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science, 2000, 290(5500): 23232326
[2] Seung H S, Lee D D. The Manifold Ways of Perception. Science, 2000, 290(5500): 22682269
[3] Tenenbaum J B, de Silva V, Langford J C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 2000, 290(5500): 23192323
[4] Lu J W, Plataniotis K N, Venetsanopoulos A N. Face Recognition Using LDABased Algorithms. IEEE Trans on Neural Networks, 2003, 14(1): 195200
[5] Wu Y M, Chan K L. An Extended Isomap Algorithm for Learning MultiClass Manifold // Proc of the IEEE International Conference on Machine Learning and Cybernetics. Shanghai, China, 2004, Ⅵ: 34293433
[6] Chen H T, Chang H W, Liu T L. Local Discriminant Embedding and Its Variants // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. San Diego, USA, 2005, Ⅱ: 846853
[7] Geng Xin, Zhan Dechuan, Zhou Zhihua. Supervised Nonlinear Dimensionality Reduction for Visualization and Classification. IEEE Trans on Systems, Man, and Cybernetics, 2005, 35(6): 10981107
[8] Saul L K, Roweis S T. Think Globally, Fit Locally: Unsupervised Learning of Nonlinear Manifolds. Journal of Machine Learning Research, 2003, 4(6): 119155
[9] Zhang Zhenyue, Zha Hongyuan. Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. SIAM Journal of Scientific Computing, 2004, 26(1): 313338
[10] Zhang W, King I. A Study of the Relationship between Support Vector Machine and Gabriel Graph // Proc of the International Joint Conference on Neural Networks. Honolulu, USA, 2002, Ⅰ: 239244
[11] Roweis S, Saul L K, Hinton G E. Global Coordination of Local Linear Models. Advances in Neural Information Processing System, 2002, 14(2): 889896
[12] Kim T K, Kittler J. Locally Linear Discriminant Analysis for Multimodally Distributed Classes for Face Recognition with a Single Model Image. IEEE Trans on Pattern Analysis and Machine Intelligence, 2005, 27(3): 318327
[13] Schapire R E, Freund Y, Bartlett P, et al. Boosting the Margin: A New Explanation for the Effectiveness of Voting Methods. The Annals of Statistics, 1998, 26(5): 16511686
[14] Friedman J, Hastie T, Tibshirani R. Additive Logistic Regression: A Statistical View of Boosting. The Annals of Statistics, 2000, 28(2): 337407
[15] Lu J W, Plataniotis K N, Venetsanopoulos A N. Regularization Studies of Linear Discriminant Analysis in Small Sample Size Scenarios with Application to Face Recognition. Pattern Recognition Letters, 2005, 26(2): 181191
[16] Yale University. Face Database [DB/OL]. [20051215]. http://cvc.yale.edu/projects/yalefacesB/yalefacesB.html
[17] Graham D B, Allinson N M. Characterizing Virtual Eigensignatures for General Purpose Face Recognition // Wechsler H, Phillips P J, Bruce V, eds. Face Recognition: From Theory to Applications. Berlin, Germany: SpringerVerlag, 1998: 446456 |
|
|
|
2007, Vol. 20 
