最大散度差和大间距线性投影与支持向量机

Maximum Scatter Difference,Large Margin Linear Projection and Support Vector Machines

首先对 Fisher 鉴别准则作了必要的修正，并基于新的鉴别准则设计了最大散度差分类器；然后探讨了当参数 C 趋向无穷大时，最大散度差分类器的极限情况，得到了大间距线性投影分类器；最后通过分析说明，大间距线性投影分类器实际上是在模式样本线性可分的条件下，线性支持向量机的一种特殊情况．在 ORL 和 NUST603人脸库上的测试结果表明，最大散度差分类器和大间距线性投影分类器可以与线性支持向量机、不相关线性鉴别分析相媲美，优于 Foley-Sammon 鉴别分析方法．

A modified Fisher discriminant is proposed at first. Then maximum scatter difference classifier (MSDs) which is based on the new discriminant is derived. It is showed that when parameter C in the MSDs is approaching infinity, a new kind of classifier called large margin linear projection classifier (LMLP) can be obtained. Theoretical analysis indicates that LMLP is a special case of linear support vector machines when the pattern samples are linearly separable. Experimental results conducted on the ORL and NUST603 datasets show that the MSDs and LMLP are better than traditional linear discriminant analysis methods such as Foley-Sammon linear discriminant analysis, and can compete with linear support vector machines and uncorrelated linear discriminant analysis.