Generalized semi-inner products with applications to regularized learning

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:372

Article

Zhang, Haizhang¹  Zhang, Jun¹ 

[1] Univ Michigan, Ann Arbor, MI 48109 USA

关键词: Generalized semi-inner products;    Duality mappings;    Riesz representation theorem;    Regularization networks;    Representer theorems;    Characterization equations;   

DOI  :  10.1016/j.jmaa.2010.04.075

来源: Elsevier

【 摘 要 】

We propose a definition of generalized semi-inner products (g.s.i.p.). By relating them to duality mappings from a normed vector space to its dual space, a characterization for all g.s.i.p. satisfying this definition is obtained. We then study the Riesz representation of continuous linear functionals via g.s.i.p. As applications, we establish a representer theorem and characterization equation for the minimizer of a regularized learning from finite or infinite samples in Banach spaces of functions. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free