Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Apr 2019 · American Mathematical Soc.
Ebook
122
Pages
About this ebook
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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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 imp...
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About the author
Yuesheng Xu: Syracuse University, Syracuse, NY,
Qi Ye: South China Normal University, Guangzhou, China
Yuesheng Xu: Syracuse University, Syracuse, NY,
Qi Ye: South China Normal University, Guangzhou, China
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