A learning algorithm with gaussian regularizer for kernel neuron

Abstract

In support vector machine there exist four attractive techniques: kernel idea to construct nonlinear algorithm using Mercer kernels, large margin or regularization to control generalization ability, convex objective functional to obtain unique solution, and support vectors or sparseness to reduce computation time. The kernel neuron is the nonlinear version of McCulloch-Pitts neuron based on kernels. In this paper we define a regularized risk functional including empirical risk functional and Gaussian regularizer for kernel neuron. On the basis of gradient descent method, single sample correction and momentum term, the corresponding learning algorithm is designed, which can realize four ideas in support vector machine with a simple iterative scheme and can handle the classification and regression problems effectively. © Springer-Verlag 2004.