多分辨率小波极限学习机  

Multiresolution wavelet extreme learning machine

作　　者：全丽萍[1] 李晓理[1,2] 王巧智[3] 

机构地区：[1]北京科技大学自动化学院,北京100083 [2]上海交通大学机械系统与振动国家重点实验室,上海200240 [3]北京科技大学机械工程学院,北京100083

出　　处：《北京科技大学学报》2014年第12期1712-1719,共8页Journal of University of Science and Technology Beijing

基　　金：新世纪优秀人才支持计划资助项目(NCET-11-0578);中央高校基本科研业务费专项资金资助项目(FRF-TP-12-005B);高等学校博士学科点专项科研基金资助项目(20130006110008);机械系统与振动国家重点实验室开放课题(MSV-2014-09)

摘　　要：针对一类具有空间不均匀性的辨识和回归问题,提出了基于小波分析的极限学习机方法.从多分辨率分析的思想出发,构造一簇紧支撑正交小波作为隐层激活函数,并利用改进的误差最小化极限学习机训练输出层权重,避免了新加入高分辨率子网络后的重新训练.同时,由一维多分辨分析的张量积构造了二维多分辨小波极限学习机.进而通过脊波变换将小波学习机扩展到高维空间,对脊波函数的伸缩、方向和位置参数进行优化计算.对具有奇异性的函数仿真结果证明,与标准极限学习机相比,小波极限学习机由于其聚微性能在极短的训练时间内更好地逼近目标.一些实际基准回归问题上的测试验证了脊波极限学习机在其中大部分问题上达到更高的训练和泛化精度.An extrme learning machine（ ELM） algorithm based on wavelet transform was designed for a class of indentification and regression problem with inhomogeneity in a space. From the standpoint of multiresolution analysis,a set of compactly supported orthogonal wavelets was constructed as the hidden layer activation function,and the output layer weight of the network was trained by an error minimized extreme learning machine. This method avoided retraining the output layer parameter as adding a subnetwork with higher resolution. The wavelet ELM was then extended into a two-dimensional space using the tensor product of a scaling function. To hurdle high-dimensionality issues,ridgelet transform based on ELM was obtained,whose scaling,direction,and position parameters were determined by optimization methods. Simulation results on functions with singularity confirm that the wavelet ELM can approch the target better. When being tested on some real benchmark problems,the ridgelet ELM demonstrates better training and testing accuracy on most cases.

关 键 词：学习算法 极限学习机 小波分析 多分辨分析 正交 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]