Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Released on by Yuesheng Xu
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  • Generalized Mercer Kernels and Reproducing Kernel Banach Spaces Book Detail

  • Author : Yuesheng Xu
  • Release Date : 2019-04-10
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 134
  • ISBN 13 : 1470435500
  • File Size : 85,85 MB
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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces by Yuesheng Xu PDF Summary

Book Description: This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .

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