Multiscale Support Vector Regression Method On Spheres with Data Compression

In this manuscript, we investigate the multiscale support vector regression (SVR) method with data compression for approximation of functions on the unit sphere. The data are obtained at scattered sites on the sphere and may contain noise. The Vapnik ε-intensive loss function, which has been well-developed in learning theory, is introduced to obtain a local regularized approximation at each step, a data compression method is applied to discard small coefficients during the computation. We will 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 support the theoretical predictions.