Varying-scale Support Vector Regression Method

In this paper, we investigate the varying-scale support vector regression(SVR) method for approximation of functions in Sobolev spaces on bounded domains, which utilizes radial basis function to approximate an unknown function defined on arbi-trary dimensions with arbitrary smoothness. We proved convergence of Varying-scale ∈-SVR method which approximates the target function in smooth function space for noisy measurement, and extended Varying-scale ∈-SVR to Varying-scale V-SVR, we also proved convergence of Varying-scale V-SVR. The results of some numerical examples shows the robustness of Varying-scale V-SVR algorithm.