摘要
利用 Fisher鉴别准则函数即为广义 Rayleigh商这一特点 ,首先分析了广义 Rayleigh商的极值性质 ,指出以共轭正交的约束条件代替 Foley- Sammon正交条件的合理性 .然后利用广义特征方程存在共轭正交的特征向量这一结论 ,巧妙地解决了该共轭正交条件下最优鉴别矢量集的求解问题 .从理论上分析了该最优鉴别矢量集较经典的 Foley- Samm on最优鉴别矢量集以及 Fisher线性鉴别法的优越性 .另外 ,进一步讨论了在小样本情况下 ,类内散布矩阵奇异时鉴别矢量集的求解问题 ,并给出了简单易行的算法 .最后 ,在 CENPARMI手写体阿拉伯数字库和ORL 标准人脸库上的试验结果证实了算法的有效性和稳定性 .
In this paper important theories are developed based on the fact that the Fisher discriminant criterion function is a generalized Rayleigh quotient in essence. The extremum properties of generalized Rayleigh quotient are first analyzed and it is pointed out that it is rational to use conjugate orthogonal constraints instead of orthogonal constraints. Then the problem of finding the optimal discriminant vectors subjected to such constraints is solved using the property that there exist a set of conjugate orthogonal eigenvectors satisfying the generalized eigen-equation. Furthermore, it is pointed out that the theories in this paper is a progress of classical Fisher linear discriminant, and the optimal discriminant vectors presented are better than Foley-Sammons' in a sense. Furthermore, how to calculate optimal discriminant vectors in case of the within-class scatter matrix being singular is discussed and a simple approximate algorithm is given. The results of experiments on Concordia University CENPARMI handwriting numeral database and Olivetti Research Laboratory (ORL) face database show that the algorithms presented are efficient and robust.
出处
《计算机研究与发展》
EI
CSCD
北大核心
2001年第11期1331-1336,共6页
Journal of Computer Research and Development
基金
国家自然科学基金资助 ( 60 0 72 0 34 )
关键词
特征抽取
图像识别
人脸识别
最优鉴别特征
目标函数
Fisher discriminant criterion, optimal discriminant vectors, feature extraction, numeral and face recognition
