基于张量积结构的多维小波网络（英文）

Multidimensional Wavelet Networks Based on a Tensor Product Structure

中文关键词  小波框架  多维小波  张量积结构  函数逼近

英文关键词  wavelet frames  multidimensional wavelets  tensor product structure  function approximation

中文摘要

      针对多维函数逼近的‘维数灾’问题, 依据小波框架理论提出了一种张量积结构小波网络, 其主要特点是在网络输出层将各维输入的小波重构相乘, 从而得到自动覆盖函数输入空间的多维小波框架, 最后通过权系数的在线或离线学习实现多维函数的小波逼近. 理论分析和仿真结果证实了该结构设计方法应用于多维函数逼近时的有效性.

英文摘要

      Based on the wavelet frame theory, a novel wavelet network for function learning in multidimensional spaces is proposed to avoid the 'curse of dimensionality'. The main feature of the proposed wavelet network is to multiply the reconstruction of each dimension in the output layer instead of adding them as usual. Thus a multidimensional wavelet frame will be generated automatically for approximation, and function learning can be realized through online or off-line adjustment of corresponding weight coefficients. Design methods for one_dimensional wavelet networks can also be generalized straightforwardly to multidimensional cases by using the tensor product structure. In the experiments, the multidimensional wavelet network performs well.