小波神经网络逼近非线性函数算法

介绍用于函数近似的一种新型神经网络——小波神经网络,该小波神经网络采用的函数是sigmoid函数的组合.文中从理论上阐明了小波神经网络对某些时频有限的非线性函数的逼近能力,并实际建立了一个前馈小波神经网络,同时讨论了如何选择小波母函数及如何减少该神经网络规模的算法.实验结果表明这种小波神经网络可以在较小规模的基础上实现对这类非线性函数的逼近.

The Algorithm of the Wavelet Network for Nonlinear Function Approximation

In this paper, we use a new type of network, wavelet network, to approximate a nonlinear function. The wavelet network is studied with the combination of the traditional neural network theory with the most advanced math tool of analysis and it contains wavelons whose activation function is wavelet constructed with sigmoid function. This paper illuminates the approximation theory of the wavelet network and constructs a practical wavelet network. We also discuss the choice of the mother wavelet and the algorithm of decreasing the number of wavelons. The experimental results show that the wavelet network has achieved a high accuracy for approximating nonlinear function, and the scale of the network is small.