Sparse training procedure for kernel neuron

The kernel neuron is the generalization of classical McCulloch-Pitts neuron using Mercer kernels. In order to control generalization ability and prune structure of kernel neuron, we construct a regularized risk functional including both empirical risk functional and Laplace regularization term in this paper. Based on the gradient descent method, a novel training algorithm is designed, which is referred to as the sparse training procedure for kernel neuron. Such a procedure can realize three main ideas: kernel, regularization (or large margin) and sparseness in the kernel machines (e.g. support vector machines, kernel Fisher discriminant analysis, etc.), and can deal with the nonlinear classification and regression problems effectively.