Abstract: Binary Fisher discriminant criterion，large margin linear projection criterion，and maximum scatter difference discriminant criterion are all binary linear discriminant criteria which can be directly used in pattern recognition.The common ground of these criteria is that they all determine the optimal projection axis based on the separability of projected samples.The differences are their definitions of the separability of projected samples.Previous studies show that large margin linear projection classifiers and support vector machines，large margin linear projection criterion and maximum scatter difference discriminant criterion，and maximum scatter difference discriminant criterion and binary Fisher discriminant criterion are closely related.Based on previous results，discover the intrinsic relationships between these criteria and establish an overall framework for these binary linear discriminant criteria based on the separability of projected samples in this paper.

Key words: binary Fisher discriminant criterion, large margin linear projection criterion, maximum scatter difference discriminant criterion, multiple objective programming

摘要： 两类Fisher鉴别准则、大间距线性投影准则以及最大散度差鉴别准则都是直接用于模式分类的两类线性鉴别准则，它们的共同点是将“投影后数据的可分性达到最大的方向”作为最优投影方向。区别在于它们对数据可分性的定义有所不同。过去的研究成果表明，大间距线性投影分类器与支持向量机之间、大间距线性投影准则与最大散度差鉴别准则之间以及最大散度差鉴别准则与两类Fisher鉴别准则之间，均存在着这样或那样的联系。论文试图在以往研究成果的基础上进一步理清这些两类线性鉴别准则之间的内在关系，并建立一个统一的理论框架从而将基于投影后数据可分性的这些两类线性鉴别准则都纳入其中。

关键词: 两类Fisher鉴别准则, 大间距线性投影准则, 最大散度差鉴别准则, 多目标规划