两步降维的核主成份分析(kernel principal component analysis,KPCA)+线性判别式分析(linear discriminantanalysis,LDA)法中,第一步KPCA变换阵的选取影响数据的分类结果。对线性不可分问题首先研究了正定核KPCA+LDA中KPCA变换阵的选...两步降维的核主成份分析(kernel principal component analysis,KPCA)+线性判别式分析(linear discriminantanalysis,LDA)法中,第一步KPCA变换阵的选取影响数据的分类结果。对线性不可分问题首先研究了正定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;其次,将正定核推广到不定核,研究了不定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;最后通过实验加以分析和验证。展开更多
The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used t...The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.展开更多
文摘两步降维的核主成份分析(kernel principal component analysis,KPCA)+线性判别式分析(linear discriminantanalysis,LDA)法中,第一步KPCA变换阵的选取影响数据的分类结果。对线性不可分问题首先研究了正定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;其次,将正定核推广到不定核,研究了不定核KPCA+LDA中KPCA变换阵的选取对分类结果的影响;最后通过实验加以分析和验证。
基金Supported by the National Natural Science Foundation of China(60473035)~~
文摘The relationship among Mercer kernel, reproducing kernel and positive definite kernel in support vector machine （SVM） is proved and their roles in SVM are discussed. The quadratic form of the kernel matrix is used to confirm the positive definiteness and their construction. Based on the Bochner theorem, some translation invariant kernels are checked in their Fourier domain. Some rotation invariant radial kernels are inspected according to the Schoenberg theorem. Finally, the construction of discrete scaling and wavelet kernels, the kernel selection and the kernel parameter learning are discussed.
