隐层小波元神经网络的非线性跟踪特性

The Nonlinear Tracing Property of the Hidden Wavelet Neurons Networks

基于Hilbert空间中Lebesgue划分的特点,运用算子理论中变换的连续性和相对紧集的拓扑结构研究了小波神经网络的跟踪特性,利用作为隐层激励函数的小波函数的紧支撑和可积性,从代数分析的角度证明了只要隐层激活函数的小波函数满足相应的性质,那么小波神经网络就能以任意的精度跟踪紧集上的连续非线性函数.仿真实例表明了小波神经网络对非线性函数来说是一致跟踪器.*

In this paper, the tracking characteristics of wavelet neural networks are studied on the basis of the traits of Lebesgue partition in the Hilbert space, by using the transpositional continuity of the operator theory and the topology structure of the relatively compact set. If the wavelet function, the activation function of hidden layer, is satisfied with the corresponding properties, the wavelet neural networks can track the smooth nonlinear function in compact set with any precision. This conclusion is drawn from the view of algebraic analysis and by the compact support and integral characteristics of wavelet function. The simulation indicates that the wavelet neural network is a universal tracker to the nonlinear function.