The Study On Gauss Kernel Function In Support Vector Machine

Support Vector Machine (SVM) is the main content of Statistics Learning Theory developed from 1990s. The kernel function is the crucial ingredient of SVM. In a great of kernel functions, many researchers attach importance to Gauss kernel function because of its peculiar property and broad application.This paper mainly discusses some aspects of Gauss kernel function.First, this paper introduces Gauss kernel function through SVM and discusses its separability and the property of localization. Based the property of localization of Gauss kernel function, we select global kernel function to compound with Gauss kernel function and constitute combination kernel to improve the performance of classifier.Next, through VC dimension theory and structural risk minimization principle, we explain the importance of selecting parameter in SVM and select Gauss kernel radius and punish- parameter C.For the selecting of kernel radius, one of the known methods is the rule of Joachims' LOO error up bound. This paper suggests the rule of maximizing the ratio of within-class to between-class distance. Through emulator, we compare it with the known method and find this technique is effective.Last, this paper compares the application of Gauss kernel in SVM and RBF network and introduces the superiority of kernel fisher discriminant based Gauss kernel using in nonlinear separated data.