New algorithm for training feedforward neural networks with cubic spline weight functions

Abstract

A new learning algorithm based on the feedforward neural networks is proposed for solving the problems of interpolation.The network's topology is so simple that the number of neurons needed for solving the problem under investigation is independent of the number of patterns.The number of neurons needed for the training is simply expressed as the multiplication of the input patterns' vector dimension by the output patterns' vector dimension.Only one layer weights are trained.The trained weights consist of cubic spline functions,not constants like the popular learning algorithm such as backpropagation(BP) or radial basis function(RBF) networks.The new algorithm developed is the learning procedure to solve two systems of linear equations for getting the forms of weights' cubic spline functions,without problems such as local minima,slow convergence,and dependent on initialized values arising from the steepest descent-like algorithms.Finally,to illustrate the power of the new learning algorithm,some simulation examples are presented to show good performance in interpolation precision and training speed compared with the popular learning algorithm such as backpropagation and radial basis function networks.