Fast and Efficient Second-Order Method for Training Radial Basis Function Networks

This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.