Abstract：Uncorrelated space algorithm based on the fisher criterion function is a fast method for extracting uncorrelated discriminant vectors, but it may have the small size sample problem when applied in face recognition. And thus an improved uncorrelated space algorithm is proposed. It effectively overcomes the small size sample problem. The main idea of the proposed algorithm is to map the original space into a low dimensional subspace, and then the singularity of the total-scatter matrix can be avoided in this low dimensional subspace. It is proved that the uncorrelated discriminant vectors derived in this low dimensional subspace are equal to those derived in the original space. In addition, according to the symmetry of scatter matrix, a fast method is introduced to further speed up the computation of uncorrelated discriminant vectors. Finally, the experimental results on facial databases demonstrate the effectiveness of the proposed algorithm.
林玉娥，顾国昌，刘海波. 一种改进的不相关空间算法及其在人脸识别中的应用*[J]. 模式识别与人工智能, 2008, 21(5): 615-620.
LIN Yu-E, GU Guo-Chang, LIU Hai-Bo. An Improved Uncorrelated Space Algorithm and Its Application to Face Recognition. , 2008, 21(5): 615-620.
[1] Kirby M,Sirovich L. Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces. IEEE Trans on Pattern Analysis and Machine Intelligence, 1990, 12(1): 103-108 [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] Jin Zhong, Yang Jingyu, Zhong Shanhu, et al. Face Recognition Based on the Uncorrelated Discrimination Transformation. Pattern Recognition, 2001, 34(7): 1405-1416 [4] Yang Jingyu, Jin Zhong, Hu Zhongshan. A Theorem on Dimensionality of the Uncorrelated Optimal Discriminant Feature Space. Chinese Journal of Computers, 2003, 26(1): 110-115 (in Chinese) (杨静宇,金 忠,胡钟山.具有统计不相关性的最佳鉴别特征空间的维数定理.计算机学报, 2003, 26(1): 110-115) [5] Jing Xiaoyuan, Zhang D, Jin Zhong. UODV: Improved Algorithm and Generalized Theory. Pattern Recognition, 2003, 36(11): 2593-2602 [6] Wu XiaoJun, Yang Jingyu, Wang Shitong, et al. A Theoretical Result on the Generalized Optimal Set of Statistically Uncorrelated Discriminant Vectors. Acta Electronica Sinica, 2005, 32(10): 1720-1722 (in Chinese) (吴小俊,杨静宇,王士同,等.广义统计不相关最优鉴别矢量集的一个理论结果.电子学报, 2005, 32(10): 1720-1722) [7] Liang Zhizheng, Shi Pengfei. Uncorrelated Discriminant Vectors Using a Kernel Method. Pattern Recognition, 2005, 38(2): 307-310 [8] Chen Mianshu, Chen Hexin, Liu Wei. A New Method for Resolving the Uncorrelated Set of Discriminant Vectors. Chinese Journal of Computers, 2004, 27(7): 913-917 (in Chinese) (陈绵书,陈贺新,刘 伟.一种新的求解无相关鉴别矢量集方法.计算机学报, 2004, 27(7): 913-917) [9] Yang Jing, Yang Jingyu. Why Can LDA be Performed in PCA Transformed Space? Pattern Recognition, 2003, 36(2): 563-566 [10] 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 [11] Ye Jieping, Xiong Tao. Computational and Theoretical Analysis of Null Space and Orthogonal Linear Discriminant Analysis. Journal of Machine Learning Research, 2006, 7(10): 1183-1204
2008, Vol. 21 
