Hermite前向神经网络隐节点数目自动确定

从函数逼近论出发,构造了一类以Hermite正交基为激励函数的前向神经网络.在保证网络逼近能力的前提下,令其输入层至隐层的权值和各神经元阈值分别为1和0,导出了基于伪逆的隐层至输出层最优权值的直接计算公式.并针对Hermite前向神经网络,提出一种依照学习精度要求而逐次递增型的隐节点数自动、快速、准确的确定算法.对多个目标函数的计算机仿真和预测结果表明,该神经网络权值直接确定方法和隐节点数自动确定算法能很快地找到最优的隐节点数及其对应的最优权值,且网络具有较好的预测能力.

Number determination of hidden-layer nodes for Hermite feed-forward neural network

A new feed-forward neural network was constructed by using Hermite orthogonal polynomial as activation function, which originated from the function-approximation theory. All neural bias and weights from input to hidden layer were respectively fixed to be 0 and 1 with approximation capability guaranteed, and a pseudo-inverse based direct-determination method was derived for the optimal neural weights from hidden layer to output layer. Then an order-increasing automatic-determination algorithm was presented for the optimal number of hidden-layer neurons according to the precision requirement. Computer simulation and prediction results based on multiple target-functions show that the proposed algorithms can quickly obtain the optimal number and weights of hidden-layer neurons and have a relatively good prediction capability.