Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

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 implem...

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Bibliographic Details
Main Authors: Xu, Yuesheng, Ye, Qi
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2019
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Banach spaces
Functions of complex variables
Geometric function theory
Kernel functions
Support vector machines
Generalized Mercer Kernels
Machine Learning
Support Vector Machines
Sparse Learning Methods
Positive Definite Kernels
Reproducing Kernel Banach Spaces
ISBN:9781470435509, 1470435500
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary: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 we 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, we develop a new concept of generalized Mercer kernels to construct
Bibliography:March 2019, volume 258, number 1243 (seventh of 7 numbers)
Includes bibliographical references and index
ISBN:9781470435509
1470435500
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1243