| 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 |
| Electronic 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 258; 2019; 122 ppMSC: 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 \(1\leq p\leq\infty\).
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Table of Contents
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Chapters
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1. Introduction
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2. Reproducing Kernel Banach Spaces
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3. Generalized Mercer Kernels
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4. Positive Definite Kernels
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5. Support Vector Machines
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6. Concluding Remarks
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Acknowledgments
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Additional Material
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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 \(1\leq p\leq\infty\).
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Chapters
-
1. Introduction
-
2. Reproducing Kernel Banach Spaces
-
3. Generalized Mercer Kernels
-
4. Positive Definite Kernels
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5. Support Vector Machines
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6. Concluding Remarks
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Acknowledgments
