Hermite正交基前向神经网络的权值直接确定法

Feed-Forward Neural Network Activated with Hermite Orthogonal Polynomials and Its Weights-Determination Method

根据多项式插值与逼近理论,提出了一种基于Hermite正交基的前向神经网络模型.该神经网络采用3层前向结构,以一组Hermite正交多项式作为隐层神经元的激励函数,而输入输出层神经元则采用线性激励函数.依据误差回传(BP)算法给出了权值修正的迭代公式.区别于以往反复迭代训练而达到最优权值的标准做法,针对该Hermite正交基前向神经网络模型,进一步提出了一种基于伪逆的直接计算权值的方法(即一步确定).该权值直接确定法避免了以往的权值反复迭代的冗长训练过程,仿真结果显示其具有比传统的BP迭代法更快的计算速度和工作精度.

Based on polynomial-interpolation and curve-fitting th work using Hermite orthogonal polynomial activation-functions is el adopts a three-layer structure, where the hidden-layer neurons eory, a special feed-forward neural net- proposed in this paper. The neural modare activated by a group of Hermite orthogonal polynomial functions, while the input and output layers＇ neurons employ linear activation functions. In our research, we first derive its weights-updating formula by adopting the standard BP training algorithm. More importantly, a pseudo inverse-based method is then proposed which could immediately determine the network weights without iterative training. Computer-simulation results show that the immediate-weights-determination method could be more efficient and accurate than the conventional BP itera- tive-training method.