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| A Generalized Form of Fisher Linear Discriminant Function |
| CHENG Zheng-Dong1,2, ZHANG Yu-Jin1, FAN Xiang2,3 |
1.Department of Electronic Engineering, Tsinghua University, Beijing 100084
2.Department of Photoelectricing, Electronic Engineering Institute, Hefei 230037
3.Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230027 |
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Abstract A generalized form of Fisher discriminant function is presented. It overcomes the limitations of two common discriminant functions. The presented form uniforms the discriminant functions in two subspaces of the dual subspace discriminant analysis (DSDA). A new orthogonal discriminant vector set is obtained by QR decomposition, and its discriminant property is approximate to that of the Foley-Sammon orthogonal discriminant vector set with smaller computational complexity. The experiments on ORL and JAFFE database show that theory analysis is consistent to the experimental results.
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Received: 16 November 2007
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[1] Fisher R A. The Use of Multiple Measurements in Taxonomic Problems. Annual of Eugenics, 1936, 7: 179-188
[2] Duchene J, Leclercq S. An Optimal Transformation for Discriminant and Principal Component Analysis. IEEE Trans on Pattern Analysis and Machine Intelligence, 1988, 10(6): 978-983
[3] Cheng Yunpeng. Matrices Theory. 2nd Edition. Xi'an, China: Northwestern Polytechnical University Press, 2001 (in Chinese)
(程云鹏.矩阵论.第2版.西安:西北工业大学出版社, 2001)
[4] Foley D H, Sammon J W. An Optimal Set of Discriminant Vectors. IEEE Trans on Computers, 1975, 24(3): 281-289
[5] Liu Ke, Cheng Yongqing, Yang Jingyu, et al. An Efficient Algorithm for Foley-Sammon Optimal Set of Discriminant Vectors by Algebraic Method. International Journal of Pattern Recognition and Artificial Intelligence, 1992, 6(5): 817-829
[6] Wang Xiangang, Tang Xiaoou. Dual-Space Linear Discriminant Analysis for Face Recognition // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, USA, 2004, Ⅱ: 564-569
[7] Yang Jian, Yang Jingyu. Why Can LDA Be Performed in PCA Transformed Space? Pattern Recognition, 2003, 36(2): 563-566
[8] Yu Hua, Yang Jie. A Direct LDA Algorithm for High-Dimensional Data with Application to Face Recognition. Pattern Recognition, 2001, 34(10): 2067-2070
[9] Yang Jian, Yang Jingyu, Liu Ningzhong. Theory and Algorithm of Uncorrelated Optimal Discriminant Analysis. Journal of Nanjing University of Science and Technology: Natural Science, 2002, 26(2): 179-182 (in Chinese)
(杨 健,杨静宇,刘宁钟.统计不相关最优鉴别分析的理论与算法.南京理工大学学报:自然科学版, 2002, 26(2): 179-182)
[10] Lyons M J, Budynek J, Akamastu S. Automatic Classification of Single Facial Images. IEEE Trans on Pattern Analysis and Machine Intelligence, 1999, 21(12): 1357-1362
[11] de Olivier V, Aeberhardsl S. Line-Based Face Recognition under Varying Pose. IEEE Trans on Pattern Analysis and Machine Intelligence, 1992, 21(10): 1081-1088
[12] Wang Haixian, Zheng Wenming, Hu Zilan. Local and Weighted Maximum Margin Discriminant Analysis // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Minneapolis, USA, 2007, Ⅰ: 1-8
[13] Jin Zhong, Yang Jingyu, Hu Zhongshan. Effective Extraction of Optimal Discriminant Features and the Dimension Problem. Chinese Journal of Computers, 2000, 23(1): 108-112 (in Chinese)
(金 忠,杨静宇,胡钟山.有效最佳鉴别特征的抽取与维数问题.计算机学报, 2000, 23(1): 108-112) |
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2009, Vol. 22 
