A multiscale support vector regression method on spheres with data compression

We propose and analyze a multiscale support vector regression algorithm for noisy scattered data on the unit sphere. To this end, the algorithm uses Wendland's radial basis functions with different scales and the Vapnik -intensive loss function to compute a regularized approximation at each step. A data compression method was applied to discard small coefficients dynamically. We discuss the convergence of the algorithm and prove additional errors can be controlled so that the discarding strategy does not lead to significant errors. Numerical simulations which support the theoretical results will be presented.