一种变形Fisher判别准则函数及最优判别向量集

An Approved Fisher Discriminant Criterion Function and Its Corresponding Optimal Set of Discriminant Vectors

基于Fisher判别准则函数式,提出了一种无约束的最优判别矢量集,并给出了求解算法,另外,当训练样本矢量数小于样本矢量维数(即小样本问题),类内散布矩阵奇异,此时求F-S最优判别向量集及文中提出的无约束的最优判别矢量集都已不可行,对此提出了一种变形的Fisher判别准则函数,并给出了求解最优判别向量集算法。用ORL标准人脸库进行实验,实验结果表明,提出的两种最优判别向量集都有良好的分类能力。

This paper presents an optimal set of discriminant vectors which need not fill any constraint condition, and the way of how to get the set too. In addition, when the number of training samples is smaller than the dimensions of training samples（i.e, small number of training samples problem）, the within-class scatter matrix is singular. Under this circumstance, to acquire both F-S optimal set of discriminant vectors and unconstrained optimal set of discriminant vectors presented here is unfeasible. To solve this problem, an approved Fisher discriminant function is presented. The result of experiment on ORL face database shows that the algorithms presented here have strong discriminability.