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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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Xu, Yuesheng (Autor), Ye, Qi, 1983- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, 2019.
Colección:Memoirs of the American Mathematical Society ; no. 1243.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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< <∞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< <∞
  • 5.3. Support Vector Machines in 1-norm Reproducing Kernel Banach Spaces5.4. 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