一种多维小波网络的构造性算法

A Multi-Dimensional Wavelet Network Construction Algorithm

在探索单尺度径向小波框架与径向基函数网络对函数逼近特性相似的基础上 ,构造了单尺度径向基小波网络 .针对在高维应用中出现的维数灾难 ,以减少其对维数的依赖性为出发点 ,实现了限制网络规模过大的方法 ,主要包括根据输入样本的时频信息和小波的时频定位区间 ,采取多种措施自适应地从小波栅格中挑选恰当的小波基 ;根据输出样本信息 ,考虑权值的不同重要程度 ,利用自适应正交投影算法完成了网络结构大小及其连接权值的自动确定 .通过将该方法应用到脑电逆问题的求解实例中 。

Based on the single scaling wavelet frame theory and radial basis function neural network, a multi dimensional input and output wavelet network is constructed. To avoid the curse of dimensionality occurring in its many dimensional implementation, the algorithms which lessen sensitively to dimension is developed. The main idea includes: (a) selection of suitable wavelets within regular wavelet lattice according to the time frequency information of input samples and localization of wavelets; and (b) an adaptive orthogonal projective algorithm which can automatically determine the network size and calculate the network parameters in the light of the information given by output samples. The proposed algorithms can be applied to solve the electroencephalogram inverse problem, and satisfactory experimental results are obtained.