The Variant of Gaussian Kernel and Its Model Selection Method

The classification problem by nonlinear support vector machine with kernel function is discussed in this paper. The stretching ratio is defined in order to analyze the performance of the kernel function. A new type of kernel function is introduced by modifying the Gaussian kernel, and it has many properties as good as or better than Gaussian function. For example, the map of the new kernel function magnifies the distance between vectors in local because the stretching ratio is always larger than one without enlarging the radius of the circumscribed hypersphere that includes the whole mapping vectors in feature space, which gets the bigger margin. Two criterions are proposed to choose a good spread parameter for a given kernel function approximately but easily. Some experiments are given to compare the classification performances between the proposed kernel function and Gaussian kernel function.