A multiscale support vector regression method on spheres with data compression

ABSTRACT

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 $ϵ$-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.

KEYWORDS:

• Inverse problem
• multiscale algorithm
• sphere
• regularization

AMS SUBJECT CLASSIFICATIONS:

• 65F22
• 46E35

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author M. Zhong was supported by the National Natural Science Foundation of China [grant number 11501102] and Natural Science Foundation of Jiangsu Province [grant number BK20150594]. The author W. Wang was supported by the National Natural Science Foundation of China [grant number 11401257].