一种改进Fisher准则的线性鉴别分析方法

Linear discriminant analysis based on improved Fisher criterion

目前线性鉴别分析以Fisher准则或是逐对类加权Fisher准则为依据,但前者不能限制离群类,后者计算量大,鉴于此,提出一种改进Fisher准则用于线性鉴别分析。回顾了Fisher准则和逐对类加权Fisher准则,指出其中问题产生的根本原因。提出类距离和类离群程度的定义,以类距离为依据判定各类离群程度,以类离群程度为参数赋予各类权值,重新计算总体类均值和类间离散度矩阵,以得到限制离群类、突出常规类的改进Fisher准则。这种改进Fisher准则计算简单,能有效限制离群类。

Traditional linear discriminant analysis is based on Fisher criterion or weighted pairwise Fisher criterion. The former can’t restrain outlier classes, and the latter has high computation complexity, for that, a new improved Fisher criterion for linear discriminant analysis is presented. Fisher criterion and weighted pairwise Fisher criterion are reviewed. Reasons for their draw-backs are pointed out. Class distance and class outlier level are defined. Class outlier level is based on class distance. Each class is given weights for its outlier level, so as to re-estimate global mean vector and between-class scatter matrix, in order to get the new improved Fisher criterion which emphasizes less on outlier classes and more on normal classes. The improved Fisher criterion can restrain outlier classes without high computation complexity.