An Optimal Method on Uncorrelated Discriminant Vectors Based on Perturbation Analysis
WANG WeiDong1,2, ZHENG YuJie1, YANG JingYu1
1.Department of Computer Science, Nanjing University of Science and Technology, Nanjing 210094 2.School of Electronics and Information, Jiangsu University of Science and Technology, Zhenjiang 212003
Abstract：This paper, on the basis of uncorrelated image projection discriminant analysis, focuses on perturbation features of eigenvalue and eigenvector, pointing out eigenvector of morbid eigenvalue may be perturbed to a great degree. So, if the eigenvector is used as a projection axis to project, the feature vectors achieved cannot provide valid discriminant information. Therefore, an optimal method to uncorrelated discriminant vectors is proposed in this paper. And the method is tested on ORL face database. The experimental results indicate the method can simplify projection matrix, improve the efficiency of features extraction and then make the recognition ratio robust. Moreover, this paper suggests the optimal method based on perturbation analysis is suitable for optimizing other linear discriminant vectors.
王卫东，郑宇杰，杨静宇. 基于扰动分析的不相关鉴别矢量集优化方法[J]. 模式识别与人工智能, 2006, 19(3): 312-317.
WANG WeiDong, ZHENG YuJie, YANG JingYu. An Optimal Method on Uncorrelated Discriminant Vectors Based on Perturbation Analysis. , 2006, 19(3): 312-317.
[1] Foley D H, Jr Sammon J W. An Optimal Set of Discriminant Vectors. IEEE Trans on Computers, 1975, 24(3): 281-289 [2] Liu C J, Wechsler H. Robust Coding Schemes for Indexing and Retrieval from Large Face Databases. IEEE Trans on Image Processing, 2000, 9(1): 132-137 [3] Jin Z, Yang J Y, Hu Z S, Lou Z. Face Recognition Based on Uncorrelated Discriminant Transformation. Pattern Recognition, 2001, 34(7): 1405-1416 [4] 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 [5] Hong Z Q, Yang J Y. Optimal Discriminant Plane for a Small Number of Samples and Design Method of Classifier on the Plane. Pattern Recognition, 1991, 24(4): 317-324 [6] Liu K, Cheng Y Q, Yang J Y. 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 [7] Yu H, Yang J. A Direct LDA Algorithm for High-Dimensional Data with Application to Face Recognition. Pattern Recognition, 2001, 34(10): 2067-2070 [8] Zhao W Y. Performance Perturbation Analysis of Eigen-Systems. Pattern Recognition, 2000, 2(2): 105-108 [9] Yang J. Yang J Y. Uncorrelated Image Projection Discriminant Analysis and Face Recognition. Journal of Computer Research and Development, 2003, 40(3): 447-452 (in Chinese) (杨 健, 杨静宇. 具有统计不相关性的图像投影鉴别分析及人脸识别. 计算机研究与发展, 2003, 40(3): 447-452) [10] Fukunaga K. Statistical Pattern Recognition. New York, USA: Academic Press, 1989 [11] Golub G H, van Loan C F. Matrix Computations. Baltimore, USA: The John Hopkins University Press, 1989 (Golub G H, van Loan C F,著;袁亚湘,等,译. 矩阵计算.北京:科学出版社, 2001) [12] Sun J G. Matrix Perturbation Analysis. 2nd Edition. Beijing, China: Science Press, 2001 (in Chinese) (孙继广.矩阵扰动分析.第2版.北京:科学出版社, 2001) [13] Yang J, Yang J Y, Jin Z. A Feature Extraction Approach Using Optimal Discriminant Transform and Image Recognition. Journal of Computer Research and Development, 2001, 38(11): 1331-1336 (in Chinese) (杨 健,杨静宇,金 忠.最优鉴别特征的抽取及图像识别.计算机研究与发展, 2001, 38(11): 1331-1336) [14] Jin Z, Yang J Y, Lu J F. An Optimal Set of Uncorrelated Discriminant Features. Chinese Journal of Computers, 1999, 22(10): 1105-1108 (in Chinese) (金 忠,杨静宇,陆建峰.一种具有统计不相关性的最优鉴别矢量集.计算机学报, 1999, 22(10): 1105-1108)
2006, Vol. 19 
