基于傅立叶变换的变元可分离核函数的确定方法

利用傅立叶变换分析的方法提出了支持向量机理论中核函数与傅立叶变换的关系 ,并就两者的关系给出了一些有意义的新定理和相关的证明 ,证明了基于傅立叶变换的核函数在一定条件下必定满足Mercer条件 .在这些重要结论的基础上 ,可利用傅立叶变换分析核函数的特性 ,确定核函数 .特别是当核函数的变元可分离时 ,傅立叶变换在核函数分析中的意义就更加重要

Resolution to Kernel Function with Dissociable Variables Based on Fourier Transform

This paper presents a new solution that describes relations between kernel funct ions based on support vector machines (SVM) theory and Fourier transform by Four ier analysis, and proposes some new significant theorems and the relevant proofs . The paper also makes the conclusion that Mercer condition can be certainly sat isfied if Kernel functions are based on Fourier transform under specific conditi on. On the basis of these important conclusions, property of kernel functions ca n be analyzed and the kernel functions can be determined by Fourier analysis. Pa rticularly, when kernel function variables are dissociable, Fourier transform wi ll be much more significant in the kernel function analysis.