核主元分析及其在人脸识别中的应用

传统的基于数据二阶统计矩的特征脸法(Eigenface)或主元分析法(PCA)是一种有效的数据特征提取方法，是基于原始特征的一种线性变换。但是，当原始数据中存在非线性属性时，用主元分析法后留下的显著成分就可能不再反映这种非线性属性。而核主元分析则是基于原始数据的高阶统计量，是一种非线性变换，在图像识别中它可以描述多个像素之间的相关性。该文采用KPCA法提取人脸特征，利用线性支持向量机设计分类器，实验结果表明，基于核主元分析方法的识别正确率明显优于基于主元分析法。

Kernel Principal Component Analysis and Application in Face Recognition

Eigenface or principal component analysis(PCA) as a method of feature extraction demonstrates their success in face recognition, detection and tracking. The representation in PCA is based on the second order statistics of the image set, and does not describe the nonlinear relationship among the pixels. While kernel principal component analysis(KPCA) based on the higher order statistics of the images set can address the higher statistical dependencies such as the relationship among three or more pixels. Empirical results show that KPCA outperforms the Eigenface method in our face recognition.