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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Bibliographische Detailangaben
Hauptverfasser: Xu, Yuesheng, Ye, Qi
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2019
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
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-Zugang:Volltext
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Inhaltsangabe:
  • Introduction -- Reproducing Kernel Banach Spaces -- Generalized Mercer Kernels -- Positive Definite Kernels -- Support Vector Machines -- Concluding Remarks -- Acknowledgments
  • Cover -- Title page -- Chapter 1. Introduction -- 1.1. Machine Learning in Banach Spaces -- 1.2. Overview of Kernel-based Function Spaces -- 1.3. Main Results -- Chapter 2. Reproducing Kernel Banach Spaces -- 2.1. Reproducing Kernels and Reproducing Kernel Banach Spaces -- 2.2. Density, Continuity, and Separability -- 2.3. Implicit Representation -- 2.4. Imbedding -- 2.5. Compactness -- 2.6. Representer Theorem -- 2.7. Oracle Inequality -- 2.8. Universal Approximation -- Chapter 3. Generalized Mercer Kernels -- 3.1. Constructing Generalized Mercer Kernels -- 3.2. Constructing -norm Reproducing Kernel Banach Spaces for 1&lt -- &lt -- ∞ -- 3.3. Constructing 1-norm Reproducing Kernel Banach Spaces -- Chapter 4. Positive Definite Kernels -- 4.1. Definition of Positive Definite Kernels -- 4.2. Constructing Reproducing Kernel Banach Spaces by Eigenvalues and Eigenfunctions -- 4.3. Min Kernels -- 4.4. Gaussian Kernels -- 4.5. Power Series Kernels -- Chapter 5. Support Vector Machines -- 5.1. Background of Support Vector Machines -- 5.2. Support Vector Machines in -norm Reproducing Kernel Banach Spaces for 1&lt -- &lt -- ∞ -- 5.3. Support Vector Machines in 1-norm Reproducing Kernel Banach Spaces -- 5.4. Sparse Sampling in 1-norm Reproducing Kernel Banach Spaces -- 5.5. Support Vector Machines in Special Reproducing Kernel Banach Spaces -- Chapter 6. Concluding Remarks -- Acknowledgments -- Bibliography -- Index -- Back Cover