, Volume 56, Issue 4, pp 861-876
Date: 18 Nov 2012

Learning rates of regularized regression on the unit sphere

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Abstract

This paper addresses the learning algorithm on the unit sphere. The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel. The excess error can be estimated by the sum of sample errors and regularization errors. Our study shows that by introducing a suitable spherical harmonics kernel, the regularization parameter can decrease arbitrarily fast with the sample size.