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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
 
Yuesheng Xu Syracuse University, Syracuse, NY
Qi Ye South China Normal University, Guangzhou, China
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Softcover ISBN:  978-1-4704-3550-9
Product Code:  MEMO/258/1243
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5077-9
Product Code:  MEMO/258/1243.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3550-9
eBook: ISBN:  978-1-4704-5077-9
Product Code:  MEMO/258/1243.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Yuesheng Xu Syracuse University, Syracuse, NY
Qi Ye South China Normal University, Guangzhou, China
Softcover ISBN:  978-1-4704-3550-9
Product Code:  MEMO/258/1243
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5077-9
Product Code:  MEMO/258/1243.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3550-9
eBook ISBN:  978-1-4704-5077-9
Product Code:  MEMO/258/1243.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2582019; 122 pp
    MSC: Primary 68; 94; Secondary 46

    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 \(1\leq p\leq\infty\).

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Reproducing Kernel Banach Spaces
    • 3. Generalized Mercer Kernels
    • 4. Positive Definite Kernels
    • 5. Support Vector Machines
    • 6. Concluding Remarks
    • Acknowledgments
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2582019; 122 pp
MSC: Primary 68; 94; Secondary 46

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 \(1\leq p\leq\infty\).

  • Chapters
  • 1. Introduction
  • 2. Reproducing Kernel Banach Spaces
  • 3. Generalized Mercer Kernels
  • 4. Positive Definite Kernels
  • 5. Support Vector Machines
  • 6. Concluding Remarks
  • Acknowledgments
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.