Multiwavelet neural network and its approximation properties
Multiwavelet neural network and its approximation properties
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DOI：
10.1109/72.950135
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发表时间：
2001-09-01
影响因子：
--
通讯作者：
Fang, YW
中科院分区：
文献类型：
--
作者：
Jiao, LC;Pan, J;Fang, YW
提出了一种基于多小波的神经网络模型。证明了它的普适性、L-2逼近性和相容性，并估计了与这些性质相关的收敛速度。该网络的结构类似于小波网络，不同之处在于这里的正交尺度函数被正交多尺度函数代替。理论分析表明，多小波网络比小波网络具有更快的收敛速度，特别是对于光滑函数。为了比较这两种网络，分别用Lemarie-Meyer小波网络、Daubechies 2小波网络和GHM多小波网络进行了实验，实验结果与理论分析相吻合。此外，结果还表明，在跳跃间断处，两种网络的逼近性能大致相同。
A model of multiwavelet-based neural networks is proposed. Its universal and L-2 approximation properties, together with its consistency are proved, and the convergence rates associated with these properties are estimated. The structure of this network is similar to that of the wavelet network, except that the orthonormal scaling functions here are replaced by orthonormal multiscaling functions. The theoretical analyses show that the multiwavelet network converges more rapidly than the wavelet network, especially for smooth functions. To make a comparison between both networks, experiments are carried out with the Lemarie-Meyer wavelet network, the Daubechies2 wavelet network and the GHM multiwavelet network, and the results support the theoretical analysis well. In addition, the results also illustrate that at the jump discontinuities, the approximation performance of the two networks are about the same.