Robust Wavelet Support Vector Machine for Regression Estimation

As we know, M-estimation as objective function can be used to tackle this problem that the performance of wavelet network (WN) is affected by gross error severely, but its influence function is determined by the absolute value of residual, so a key problem is how to choose initial parameters. In this paper combining robust estimation with wavelet support vector machine (WSVM), a robust wavelet support vector regression (WSVR) model is developed. Firstly, a new type of wavelet support vector machine is proved and used to determine appropriate WN structure and initial parameters. It can ensure that there should be bigger absolute value of residual for sample with gross error than that for believable sample; Secondly, M-estimation is used as cost function and a method used to determine the threshold adaptively is put forward, then gradient descent is adopted to tune WN parameters. Simulations illustrate that the regression model not only has the multiscale approximation, but also better robustness and generalization, but for some special case, WSVR in single scale can not determine appropriate WN initial parameters and robust learning is very slow, thus multiscale WSVR is worth researching.