Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-3550-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3550-9 (ISBN)
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Examines 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.
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 $1/leq p/leq/infty$.
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 $1/leq p/leq/infty$.
Yuesheng Xu, Syracuse University, NY. Qi Ye, South China Normal University, Guangzhou, China.
Introduction
Reproducing Kernel Banach Spaces
Generalized Mercer Kernels
Positive Definite Kernels
Support Vector Machines
Concluding Remarks
Acknowledgments
Index
Bibliography.
| Erscheinungsdatum | 02.03.2019 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 205 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-3550-0 / 1470435500 |
| ISBN-13 | 978-1-4704-3550-9 / 9781470435509 |
| Zustand | Neuware |
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