样条权函数神经网络的一种新型算法

针对前馈神经网络在数值插值领域的应用场合,提出了一种新型结构的神经网络及其训练算法。网络拓扑结构简单,网络训练所需的神经元个数与样本个数无关,可以简单地表示成输入、输出样本向量维数之积。算法只需训练1层权函数。训练后的权函数由三次样条函数构成,而不是传统方法(反向误差传播算法“BP”或径向基函数算法“RBF”)的常数。通过求解两组线性方程组,就可以确定具体三次样条权函数形式。不存在传统梯度下降类算法的局部极小、收敛速度慢、初值敏感性等问题。仿真实验说明此算法比传统算法(如BP、RBF)精度高、速度快。

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

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.