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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.
Aiming at a class of identification and regression problems with spatial inhomogeneity, an extreme learning machine method based on wavelet analysis is proposed. From the idea of multi-resolution analysis, a cluster of compactly supported orthogonal wavelets is constructed as a hidden layer activation function, The improved error minimizes the training weight of the output layer of the limit learning machine and avoids the retraining after the new high resolution sub-network is added.At the same time, a two-dimensional multiresolution wavelet extreme learning machine is constructed from the tensor product of one-dimensional multi-resolution analysis. Then the wavelet learning machine is extended to high-dimensional space by ridgelet transform, and the stretching, orientation and position parameters of ridge-wave function are optimally calculated.The simulation results of the function with singularity show that compared with the standard limit learning machine, the wavelet limit Learning machine due to its micro-performance in a very short training time to better approaching the target.Some benchmarks on the benchmark regression problems verify the ridge wave limit learning machine in most of the problems to achieve higher training and generalization accuracy .