回归函数的小波支持向量机鲁棒估计法

小波网络具有小波的多尺度特性和神经网络的自学习功能,在回归估计中得到广泛的应用,但其性能受到样本中粗差的严重影响.虽然以M-估计作为目标函数可以解决这个问题,但由于其对应的影响函数由残差绝对值决定,因此如何选择初始参数值成为一个关键问题.为此,提出回归函数的小波支持向量机鲁棒估计方法(小波支持向量回归,WSVR,Wavelet Support Vector Regression).该方法中首先提出并证明了一种新的小波支持向量机(WSVM,Wavelet Support Vector Machine),用于确定初始参数值方法,这种方法能够确定合理的网络结构和合适的初始参数值,保证含有粗差的样本点的残差绝对值较大;然后使用一种构造的M-估计作为目标函数,并提出了自适应确定阈值方法.仿真结果表明,使用这种方法得到的回归模型不仅具有良好的多尺度逼近特性,而且有较好的鲁棒性和较高的推广性能,具有较高的理论和应用价值.

Wavelets Support Vector Machines Robust Estimate Method to Regression Function

Since wavelet network possesses both multi-scale property of wavelet and self-learning of neural network,it is widely used in regression estimation.But it is seriously affected by the gross error of samples.Although M-estimation as the object function can be used to solve the problem,its corresponding influence function is determined by the absolute value of gross error and it is a key problem to choose initial parameters.In this paper,the estimation method of regression function based on multi-wavelet support vector machine(WSVM) is put forward.This method firstly puts forward and proves a new wavelet SVM used to determine initial parameters.It can determine reasonable network structure and appropriate initial parameters,which makes sure that there is bigger absolute value of residual error of samples with gross error.Then M-estimation is used as the object function and the method used to adaptive determine the threshold is put forward.Simulation results show that regression model obtained with this method possesses not only the multi-scale approach property,but better robust property and generalization.It also possesses highly theoretical and practical values.