最优鉴别特征的抽取及图像识别

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性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-Sammon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。

A FEATURE EXTRACTION APPROACH USING OPTIMAL DISCRIMINANT TRANSFORM AND IMAGE RECOGNITION

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.