Kernel feature extraction methods observed from the viewpoint of generating-kernels

作     者：Jian YANG 

作者机构：School of Computer Science and TechnologyNanjing University of Science and TechnologyNanjing 210094China 

出 版 物：《Frontiers of Electrical and Electronic Engineering in China》 (中国电气与电子工程前沿（英文版）)

年 卷 期：2011年第6卷第1期

页      面：43-55页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Program for New Century Excellent Talents in University of China the NUST Outstanding Scholar Supporting Program and the National Natural Science Foundation of China(Grant No.60973098) 

主　　题：kernel methods feature extraction principal component analysis(PCA) Fisher linear discriminant analysis(FLD or LDA) tensor-based methods 

摘      要：This paper introduces an idea of generating a kernel from an arbitrary function by embedding the training samples into the *** on this idea,we present two nonlinear feature extraction methods:generating kernel principal component analysis(GKPCA)and generating kernel Fisher discriminant(GKFD).These two methods are shown to be equivalent to the function-mapping-space PCA(FMS-PCA)and the function-mapping-space linear discriminant analysis(FMS-LDA)methods,*** equivalence reveals that the generating kernel is actually determined by the corresponding function *** the generating kernel point of view,we can classify the current kernel Fisher discriminant(KFD)algorithms into two categories:KPCA+LDA based algorithms and straightforward KFD(SKFD)*** KPCA+LDA based algorithms directly work on the given kernel and are not suitable for non-kernel functions,while the SKFD algorithms essentially work on the generating kernel from a given symmetric function and are therefore suitable for non-kernels as well as ***,we outline the tensor-based feature extraction methods and discuss ways of extending tensor-based methods to their generating kernel versions.