Learning rates of regularized regression on the unit sphere  

作　　者：CAO FeiLong LIN ShaoBo CHANG XiangYu XU ZongBen 

机构地区：[1]Institute of Metrology and Computational Science,China Jiliang University [2]Institute for Information and System Sciences,Xi'an Jiaotong University

出　　处：《Science China Mathematics》2013年第4期861-876,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 61272023 and 61075054)

摘　　要：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.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.

关 键 词：SPHERE regularized regression spherical harmonics kernel rate of convergence 

分 类 号：O212.1[理学—概率论与数理统计]