Constructive Approximation to Multivariate Function by Decay RBF Neural Network
Constructive Approximation to Multivariate Function by Decay RBF Neural Network
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DOI：
10.1109/tnn.2010.2055888
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发表时间：
2010-09
影响因子：
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通讯作者：
Muzhou Hou;Xuli Han
中科院分区：
文献类型：
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作者：
Muzhou Hou;Xuli Han
众所周知，当网络的所有参数都是通过各种算法获得时，具有径向基函数（RBF）核的单隐层前馈网络是通用的逼近器。然而，正如在大多数神经网络实现中所观察到的那样，调整网络的所有参数可能会导致学习复杂，泛化能力差，过度训练和不稳定。与传统的神经网络理论不同，本文给出了一个具有n + 1个隐层神经元的衰减RBF神经网络可以零误差插值n + 1个多元样本的构造性证明。然后证明了给定的衰减径向基函数可以在不训练的情况下以任意精度一致逼近任何连续的多元函数。通过两个数值实验表明，该算法比传统的RBF算法、BP算法、极端学习机和支持向量机具有更快的收敛速度和更好的泛化性能。
It is well known that single hidden layer feedforward networks with radial basis function (RBF) kernels are universal approximators when all the parameters of the networks are obtained through all kinds of algorithms. However, as observed in most neural network implementations, tuning all the parameters of the network may cause learning complicated, poor generalization, overtraining and unstable. Unlike conventional neural network theories, this brief gives a constructive proof for the fact that a decay RBF neural network with n + 1 hidden neurons can interpolate n + 1 multivariate samples with zero error. Then we prove that the given decay RBFs can uniformly approximate any continuous multivariate functions with arbitrary precision without training. The faster convergence and better generalization performance than conventional RBF algorithm, BP algorithm, extreme learning machine and support vector machines are shown by means of two numerical experiments.