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| 区间小波神经网络(I)——理论与实现 |
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高协平1,2, 张 钹3,2
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1.湘潭大学数学系,湘潭,411105;2.清华大学智能技术与系统国家重点实验室,北京,100084;3.清华大学计算机科学与技术系,北京,100084
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| 摘要: |
| 本文提出了前馈神经网络学习的一种新理论——区间小波神经网络,不同于以往工作的是本工作的主要特点有:(1) 采用区间小波空间作为神经网络的学习基底空间,克服了以往神经网络基空间与被学习信号所属空间不匹配问题;(2) 由于采用区间小波理论,克服了原来被学习信号为适应神经网基空间而延拓所带来的不光滑性,使神经元数目得以节约,这在高维学习情形效果极为显著;(3) 神经单元所用活性函数不再为同一个函数. |
| 关键词: 神经网络,小波,多尺度分析. |
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| 基金项目:本文研究得到国家自然科学基金、国家863高科技项目基金和国家攀登计划基金资助. |
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| Interval-wavelets Neural Networks(I)——Theory and Implements |
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GAO Xie-ping,ZHANG Bo
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| Abstract: |
| In this paper, an interval wavelets neural networks is proposed as an alternative to feedforward neural network for approximating arbitrary nonlinear functions. Different from the past ones, the present work has main characteristics as follows: (1) using interval wavelet space as the basic learning space of neural networks, the authors have solved the problem in which basic space does not match the space of learnt signals. (2) As interval wavelets theory is used, the authors have overcome the discontinuity problem caused by enlarging learnt signals in order to adapt basic space of neural network. The number of neurons is decreased, which is greatly notable in high-dimensional situations. (3) The activity functions of neurons are not the same functions. |
| Key words: Neural network, wavelets, multiresolution analysis. |
