两输入幂激励前向神经网络权值与结构确定

基于多元函数逼近与二元幂级数展开理论,构建了一个以二元幂函数序列为隐神经元激励函数的两输入幂激励前向神经网络模型.以该网络模型为基础,基于权值直接确定法以及隐神经元数目与逼近误差的关系,提出了一种网络权值与结构确定算法.计算机仿真与数值实验结果验证了所构建的网络在逼近与去噪方面具有优越的性能,所提出的权值与结构确定算法能够快速、有效地确定网络的权值与最优结构,保证网络的最佳逼近能力.

Weights and structure determination of two-input power-activation feed-forward neural network

Based on the theory of multivariate function approximation and two-variable power series expansion, a Two-Input Power-Activation feed-forward Neural Network(TIPANN)model is constructed and studied, of which the hidden-layer neurons’activation-functions are a sequence of power functions with two variables. Moreover, based on the weights-direct-determination method and the relationship between the number of hidden-layer neurons and the neural network’s approximation error, a Weights-And-Structure-Determination(WASD)algorithm is pro- posed to determine the optimal number of hidden-layer neurons of the TIPANN. Computer simulation and numerical verification results further substantiate the superiority of the TIPANN in terms of approximation and denoising, as well as the efficacy and accuracy of the proposed WASD algorithm to determine the weights and the optimal structure of the TIPANN.