基于统计学习理论的小波神经网络优化  

Optimization of Wavelet Neural Networks Based on Statistical Learning Theory

作　　者：黄敏[1] 崔宝同[1] 顾树生[2] 

机构地区：[1]江南大学控制科学与工程研究中心,江苏无锡214122 [2]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《系统仿真学报》2006年第7期1769-1772,共4页Journal of System Simulation

基　　金：国家自然科学基金资助项目(60274024)

摘　　要：传统的离散仿射小波神经网络训练都是建立在大样本基础上的,当样本数量较少时,不能保证网络的泛化能力。在研究统计学理论的基础上,提出了以结构风险最小化为目标的训练方法。首先根据样本数据和小波基函数的时频局部化特性构造隐含层函数集,并按照小波基函数的能量大小来建立函数嵌套结构,然后采用自适应正交最小二乘法来训练网络权值,保证训练的小波神经网络结构风险最小化。仿真表明该方法不仅具有较高的收敛速度,而且最大限度地保证了网络的泛化能力。Conventional learning algorithms for a class of affine wavelet neural networks use empirical risk minimization （ERM） based on infinite samples. ERM can＇t ensure the generalization ability of network in the situation where sample size is small. A novel algorithm was proposed through using structural risk minimization （SRM） based on statistical learning theory. At first, a suitable hidden layer function set was selected according to the time-frequency information of input samples and localization of wavelets; meanwhile, a nested structure of function sets was constructed in terms of energy of wavelet basis; and then, weights of networks were optimized by adaptive orthogonal least square. Simulation results show that the novel algorithm can ensure the generalization ability of networks.

关 键 词：统计学习理论 小波神经网络 结构风险最小化 自适应正交最小二乘法 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]