利用Gaussian型RBF网络进行函数逼近的构造性估计

Constructive Estimation of Approximating of Functions with Gaus sian′s RBF Neural Network

前馈人工神经网络有着极其广泛的应用 ,如何估计隐层神经元数及相应的逼近误差 ,一直是确定前馈网络结构的难点和关键。 RBF网络是一种最重要的前馈神经网络 ,本文给出了利用 Gaussian型 RBF网络逼近连续函数或 Lebesgue-可积函数时的构造性的隐层单元数显式估算式及相应的显式逼近误差估算式。文中的结论也易于推广到离散样本的情形。这些结论对于提高 Guassian型 RBF在实际应用时的计算精度和减少计算量具有一定的指导意义。

Feed-forward artificial neural networks(ANN) a re applied very widely, and it is the key and difficulty how to estimate the numbers of units in the hidden-layer and the approximating errors. Radial basi s function(RBF) neural network is one kind of the most important feed-forward A NNs, the explicit constructive estimation of the numbers in hidden-layer(of 3 layers feed-forward ANN) and the relating errors are proposed when approximatin g continuous functions or Lebesgue integrable functions with Gauss ian′s RBF ANN are used. It is also easy for the results to be generalized to t he conditions of discrete samples. As the result, the precision of the calculati on is improved and the amount of the calculation is reduced when Gaussia n′s RBF ANN is used.