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 sigma in the Gaussian kernel is essential to generalization performance of SVMs. In this paper, determination of sigma is studied based on discussions of the influence of sigma on generalization performance. For classification problems, the optimal sigma 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 sigma, within which the generalization performance is stable. An appropriate sigma within the range can be achieved via dynamic evaluation. In addition, the lower bound of iterating step size of sigma is given. Simulation results show the effectiveness of the presented method. (C) 2002 Published by Elsevier B.V.