Approximating and learning by Lipschitz kernel on the sphere

This paper investigates some approximation properties and learning rates of Lipschitz kernel on the sphere. A perfect convergence rate on the shifts of Lipschitz kernel on the sphere, which is faster than \(\mathcal{O}(n^{ - 1/2} )\) , is obtained, where n is the number of parameters needed in the approximation. By means of the approximation, a learning rate of regularized least square algorithm with the Lipschitz kernel on the sphere is also deduced.