The estimate for approximation error of spherical neural networks

Compared with planar hyperplane, fitting data on the sphere has been an important and an active issue in geoscience, metrology, brain imaging, and so on. In this paper, with the help of the Jackson-type theorem of polynomial approximation on the sphere, we construct spherical feed-forward neural networks to approximate the continuous function defined on the sphere. As a metric, the modulus of smoothness of spherical function is used to measure the error of the approximation, and a Jackson-type theorem on the approximation is established.