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| 区间小波神经网络(ⅠⅠ)——性质与模拟 |
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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: |
| 证明了区间小波神经网络具有一致及L2逼近性质,且为相容的函数估计子,其学习收敛速度在d维情形不随d增大而减慢,本质上克服了神经网络高维学习的“维数灾难”问题,模拟实例验证了理论的正确性.
关 键 词 神经网络,小波,多尺度分析,收敛. |
| 关键词: 神经网络,小波,多尺度分析,收敛. |
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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 (ⅠⅠ)——Properties and Experiment |
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GAO Xie-ping,ZHANG Bo
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| Abstract: |
| In the present paper, it is proved that the interval wavelets neural networks has universal and L2 approximation properties and is a consistent function estimator. Convergence rates associated with these properties do not decrease as d increases in d-dimensional function learning, i.e., the “curse of dimensionality” is eliminated substantially. In the experiments, the proposed interval wavelet neural networks, compared to traditional wavelet networks, has performed better. |
| Key words: Neural network, wavelets, multiresolution analysis, convergence. |
