Frontiers of Electrical and Electronic Engineering >
Kernel feature extraction methods observed from the viewpoint of generating-kernels
Received date: 16 Jul 2010
Accepted date: 23 Nov 2010
Published date: 05 Mar 2011
Copyright
This paper introduces an idea of generating a kernel from an arbitrary function by embedding the training samples into the function. Based 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, respectively. This equivalence reveals that the generating kernel is actually determined by the corresponding function map. From 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) algorithms. The 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 kernels. Finally, we outline the tensor-based feature extraction methods and discuss ways of extending tensor-based methods to their generating kernel versions.
Jian YANG . Kernel feature extraction methods observed from the viewpoint of generating-kernels[J]. Frontiers of Electrical and Electronic Engineering, 2011 , 6(1) : 43 -55 . DOI: 10.1007/s11460-011-0129-z
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