Study On Kernel Function Of Support Vector Machine

Support Vector Machine(SVM) is the main content of Statistics Learning Theorydeveloped from1990s.Kernel function is the crucial ingredient of SVM. The selectionof the SVM-kernel with suitable form and parameters (Kernel Selection) has become akey-point both in theoretical research and application consideration. In fact, thenonlinear processing ability of SVM and the structure of the separating function areboth largely decided by the choice of individual kernel function. This paper studies theproperties and applications of Fourier kernel function and Gauss kernel function fromtwo aspects.On the one hand,we analyzes the nature of Gauss kernel and Fourier kernel indetail and show that: when the parameters of these kernels are in a specific range, SVMwith these kernel functions have the best classification error rate and optimal supportvectors. If the parameters are out of the range,it would only prolong the training time ofSVM, but the performance of SVM can not be improved additionally.On the other hand, we introduce a new variant Fourier kernel function,and analyzethe properties of the local kernel function and global kernel function.Then we alsodiscuss the characters of the form of the mixture kernels functions, and propose twonew types of mixture kernels functions. One is the conex combination of the improvedGauss kernel and Polynomial kernel,and the other one is the conex combination of Fouriorkernel and Sigmoid kernel. Experimental results show that the new mixture of kernelshave better classification performance.