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Generalized semi-inner products with applications to regularized learning

Haizhang Zhang School of Mathematics and Computational Science, Sun Yat-sen University Jun Zhang University of Michigan

mathscidoc:1609.01005

Journal of Mathematical Analysis and Applications, 372, (1), 181-196, 2010
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.
Generalized semi-inner products / Duality mappings / Riesz representation theorem / Regularization networks / Representer theorems / Characterization equations
[ Download ] [ 2016-09-20 18:24:37 uploaded by zhang ] [ 581 downloads ] [ 0 comments ] [ Cited by 4 ] 
@inproceedings{haizhang2010generalized,
  title={Generalized semi-inner products with applications to regularized learning},
  author={Haizhang Zhang, and Jun Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920182437270553031},
  booktitle={Journal of Mathematical Analysis and Applications},
  volume={372},
  number={1},
  pages={181-196},
  year={2010},
}
Haizhang Zhang, and Jun Zhang. Generalized semi-inner products with applications to regularized learning. 2010. Vol. 372. In Journal of Mathematical Analysis and Applications. pp.181-196. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920182437270553031.
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