Generalized Mercer Kernels and reproducing Kernel Banach spaces:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 258, number 1243 (seventh of 7 numbers) |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031267166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | vi, 122 Seiten |
| ISBN: | 9781470435509 |
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Datensatz im Suchindex
| _version_ | 1819253600959856640 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
1.1. Machine Learning in Banach Spaces 1
1.2. Overview of Kernel-based Function Spaces 2
1.3. Main Results 3
Chapter 2. Reproducing Kernel Banach Spaces 7
2.1. Reproducing Kernels and Reproducing Kernel Banach Spaces 7
2.2. Density, Continuity, and Separability 10
2.3. Implicit Representation 14
2.4. Imbedding 16
2.5. Compactness 21
2.6. Representer Theorem 23
2.7. Oracle Inequality 35
2.8. Universal Approximation 37
Chapter 3. Generalized Mercer Kernels 41
3.1. Constructing Generalized Mercer Kernels 41
3.2. Constructing p-norm Reproducing Kernel Banach Spaces for
1 p oo 43
3.3. Constructing 1-norm Reproducing Kernel Banach Spaces 56
Chapter 4. Positive Definite Kernels 65
4.1. Definition of Positive Definite Kernels 65
4.2. Constructing Reproducing Kernel Banach Spaces by Eigenvalues and
Eigenfunctions 65
4.3. Min Kernels 75
4.4. Gaussian Kernels 77
4.5. Power Series Kernels 83
Chapter 5. Support Vector Machines 87
5.1. Background of Support Vector Machines 87
5.2. Support Vector Machines in p-norm Reproducing Kernel Banach
Spaces for 1 p oo 90
5.3. Support Vector Machines in 1-norm Reproducing Kernel Banach
Spaces 93
5.4. Sparse Sampling in 1-norm Reproducing Kernel Banach Spaces 99
5.5. Support Vector Machines in Special Reproducing Kernel Banach
Spaces
iii
102
iv CONTENTS
Chapter 6. Concluding Remarks
Acknowledgments
Bibliography
Index
111
115
117
121
|
| any_adam_object | 1 |
| author | Xu, Yuesheng Qi, Ye |
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| id | DE-604.BV045884062 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:37:31Z |
| institution | BVB |
| isbn | 9781470435509 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031267166 |
| oclc_num | 1102429087 |
| open_access_boolean | |
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| owner_facet | DE-83 DE-29T DE-11 |
| physical | vi, 122 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spellingShingle | Xu, Yuesheng Qi, Ye Generalized Mercer Kernels and reproducing Kernel Banach spaces Memoirs of the American Mathematical Society |
| title | Generalized Mercer Kernels and reproducing Kernel Banach spaces |
| title_auth | Generalized Mercer Kernels and reproducing Kernel Banach spaces |
| title_exact_search | Generalized Mercer Kernels and reproducing Kernel Banach spaces |
| title_full | Generalized Mercer Kernels and reproducing Kernel Banach spaces Yuesheng Xu, Qi Ye |
| title_fullStr | Generalized Mercer Kernels and reproducing Kernel Banach spaces Yuesheng Xu, Qi Ye |
| title_full_unstemmed | Generalized Mercer Kernels and reproducing Kernel Banach spaces Yuesheng Xu, Qi Ye |
| title_short | Generalized Mercer Kernels and reproducing Kernel Banach spaces |
| title_sort | generalized mercer kernels and reproducing kernel banach spaces |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031267166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT xuyuesheng generalizedmercerkernelsandreproducingkernelbanachspaces AT qiye generalizedmercerkernelsandreproducingkernelbanachspaces |