The Unified Chebyshev polynomial kernel function for support vector regression machine

Support vector regression machine (SVR) has become a promising tool in many research fields, such as web intelligence, machinery fault diagnostic technique, dynamics environmental forecasting, and earthquake prediction, etc. Kernel method is most important to get more robust and higher generalization ability of SVR. In this paper, a new kernel, named Unified Chebyshev polynomial kernel (UCK), is proposed for SVR. Firstly, a group of new Unified Chebyshev polynomials are constructed using Chebyshev polynomials. Therefore, on the basis of these polynomials, a Unified Chebyshev polynomials kernel is proposed and has been proved satisfying Mercer condition. The simulation results show that UCK can lead to better generalization performance in comparison with other common kernels on many benchmark data sets.