Determination of the spread parameter in the Gaussian kernel for classification and regression

Based on statistical learning theory, Support Vector Machine (SVM) is a novel type of learning machine, and it contains polynomial, neural network and radial basis function (RBF) as special cases. In the RBF case, the Gaussian kernel is commonly used, while the spread parameter σ in the Gaussian kernel is essential to generalization performance of SVMs. In this paper, determination of σ is studied based on discussions of the influence of σ on generalization performance. For classification problems, the optimal σ can be computed on the basis of Fisher discrimination. And for regression problems, based on scale space theory, we demonstrate the existence of a certain range of σ, within which the generalization performance is stable. An appropriate σ within the range can be achieved via dynamic evaluation. In addition, the lower bound of iterating step size of σ is given. Simulation results show the effectiveness of the presented method.