Abstract:Support vector machine based on Gaussian kernel has been used in many areas. The parameter σ of the Gaussian kernel has great impact on the performance of the classifier. This paper proposes an approach to choose an optimal parameter σ based on the properties of the kernel function and the angle of geometric distance. What is more, we have solved the problem of the optimal option of the parameter σ by means of the McLaughlin expansion of the Gaussian kernel function. The experiment results indicate that this method can get parameter σ very quickly and can achieve high efficiency. Thus the difficulty of the estimation of the parameter σ can be solved by our method.