OPTIMAL FISHER DISCRIMINANT-ANALYSIS USING THE RANK DECOMPOSITION

被引:44
作者
CHENG, YQ
ZHUANG, YM
YANG, JY
机构
[1] East China Inst of Technology, Nanjing, China
关键词
OPTIMAL DISCRIMINANT VECTOR; DISCRIMINANT PLANE; FISHER DISCRIMINANT CRITERION; PATTERN ANALYSIS; MULTIVARIATE DATA ANALYSIS; PATTERN RECOGNITION;
D O I
10.1016/0031-3203(92)90010-G
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The Fisher optimal discriminant vector is a very efficient means in high-dimensional pattern analysis. In the case of a small number of samples, the within-class scatter matrix S(w) is singular; therefore, the calculation of the Fisher optimal discriminant vector becomes very important. In this paper, the conception of the rank decomposition of matrices is first introduced, and a new method for calculating the Fisher optimal discriminant vector is presented which is particularly well suited to the case of a small number of samples in the sense that the scatter matrices are rank-deficient. The new method is compared with the pseudoinverse and perturbation methods in Tian (J. Opt. Soc. Am. A 5, 1670-1672 (1988)) and Hong and Yang (Pattern Recognition 24, 317-324 (1991)). An important conclusion is proved: in the three methods, our method is the best one for calculating the Fisher optimal discriminant vectors in the cases of both a large and a small number of samples. The experimental results have also shown that our method can give the highest recognition rate in the case of a small number of samples among the three methods.
引用
收藏
页码:101 / 111
页数:11
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