Robust wavelets support vector machine estimation method for regression

Due to wavelet network with the advantage of multi-scale of wavelet and self-learning of neural network, it is widely applied in regression estimation. But it is seriously affected by the samples with gross error. Although M-estimation as object function can be used to solve the problem, its corresponding influence function is determined by the absolute value of error, thus a key problem is to choose initial parameters. In this paper, we propose an estimation method for regression function based on multiwavelet support vector machine (SVM). 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 object function and the method used to determine the threshold is put forward. Simulation results show that regression model obtained with this proposed method not only has better approximation precision, but also improves robustness and generalization. It is conduced to widening the application for wavelet network.