中文摘要：

基于泛化特征值问题的多面PSVM（GEPSVM）被O，L，Mangasarian证实是一种有效、简单、训练速度快的方法，但其仅对维数不高、样本数目也不大的数据集在实验中进行了比较和说明，而对上千维，甚至上万维人脸数据库，即小样本的、多类的问题并没有给出解决方法。文章把原算法加以改进，即把求解最小优化问题变成了求解最大优化问题，解决了因数据维数高、样本数较小而产生的奇异值问题．同时也实现了其多类算法，并用原GEPSVM算法和改进的算法来分别对这三个人脸数据库进行分类比较。从而使识别率和所用的处理时间两方面都得到了极大的改进。

英文摘要：

The effectiveness of Muhisurface Proximal SVM via generalized eigenproblem is demonstrated by tests on some simple examples or some public data sets in O.L.Mangasarian＇s paper.Although they proposed a very useful, simple and fast algorithm verified by their tests,they did not give a solution to deal with high-dimension sample sets, also the multi-class problems,just like face database.This paper gives the improved algorithm that can solve the small sample size problem which causes the singular problem,and also gives an implementation for multi-class problem.We also give the comparative results that show us the high recognition rate and low training tlme,on three public face datasets.