基于多分辨正交多小波的神经网络研究

Study of Neural Network Based on Multiresolution Orthogonal Multiwavelet

根据多小波空间中函数的多分辨率分解思想,构造了一种基于正交多小波的神经网络。该网络和小波网络结构相似,只是用同时具有紧支撑集、对称性、正交性和高阶消失矩的多尺度函数和多小波函数代替单尺度和单小波函数作为网络的激励函数。从理论上分析可得,多小波网络比单小波网络的收敛速度要快。为了比较这两种网络,对两种网络进行了对比仿真。仿真表明,实验结果和理论相吻合,另外多小波网络比单小波网络有更好的测试能力。

A model of multiwavelet neural network is proposed according to the multiresolution analysis idea in multiwavelet space in this paper. The structure of this network is similar to that of wavelet neural network, except that the orthonormal scaling functions and wavelet basis here are replaced by orthonormal multiscaling functions and multiwavelet basis, which possess compactly supported set, symmetry, orthogonality and vanishing moments at the same time. Theoretical analyses show that multiwavelet neural network con- verges more rapidly than wavelet neural network. To make a comparison between both networks, simulation experiments were cai＇ried out with wavelet neural network and muhiwavelet neural network. Simulation results support the theoretical analysis well. In addition, the results also illustrate that multiwavelet neural network is more powerful for testing than the wavelet neural network.