基于支持向量的Kernel判别分析

提出了一种新的基于支持向苗的核化判别分析方法（SV—KFD）．首先深入地分析了支持向量机（SVM）以及核化费舍尔判别分析（Kernel Fisher）方法的相互关系．基于作者证明的SVM本身所同有的零空间性质；SVM分类面的法向量在基于支持向量的类内散度矩阵条件下，具有零空间特性，提山了利用SVM的法向量定义核化的决策边界特征矩阵（Kernelized Decision Boundary Feature Matrix，KDBFM）的方法．进一步结合均值向量的差向量构建扩展决策边界特征矩阵（Ex—KDBFM）．最后以支持向量为训练集合，结合零空间方法来计算投影空间，该投影空间被用来从原始图像中提取判别特征．以人脸识别为例，作者在FERET和CAS—PEAL—R1大规模人脸图像数据怍上对所提出的方法进行了实验验证，测试结果表明该方法具有比传统核判别分析方法更好的识别性能．

Kernel Discriminant Analysis Based on Support Vectors

Discriminant analysis is one of crucial issues for the statistic-based face recognition methods. This paper proposes a novel Support Vectors based Kernel Fisher Discriminant analysis method(SV-KFD) for face recognition, which has combined the idea of the Support Vector Machine(SVM) and kernel Fiser analysis. The authors first discuss the relationship between SVM and kernel Fisher analysis. Based on the intrinsic nullspace property of the SVM proven by the authors, which shows that the normal vector of the SVM decision plane is of the nullspace property in terms of the support vectors-based within-class scatter matrix, a support vectors-based method is presented to construct the Kernelized Decision Boundary Feature Matrix (KDBFM) by using the SVM normal vectors. Furthermore the difference vector of the mean support vectors is combined to construct the Extended Kernelized Decision Boundary Feature Matrix (Ex-KDBFM). Finally, the nullspace Kernel Fisher method is exploited to seek the projection space, which is used to extract the discriminant features from the original face images. In addition, the proposed discriminant method includes two steps, and the tedious sigularity problem can be avoided. The proposed method is applied on face recognition, and the experimental results on the FERET and CAS-PEAL-R1 databases show that it performs much better than the traditional kernel discriminant analysis methods in terms of the recognition rate.