Generalized Mercer Kernels and Reproducing Kernel Banach Spaces. (Record no. 10466)
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| fixed length control field | 04073nam a22005053i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5770276 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113715.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2019 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470450779 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470435509 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5770276 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5770276 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1096284280 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA353.K47 .X8 2019 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.732 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Xu, Yuesheng. |
| 245 10 - TITLE STATEMENT | |
| Title | Generalized Mercer Kernels and Reproducing Kernel Banach Spaces. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2019. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (134 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.258 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Kernel functions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometric function theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Banach spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Functions of complex variables. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Support vector machines. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Ye, Qi. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Xu, Yuesheng |
| Title | Generalized Mercer Kernels and Reproducing Kernel Banach Spaces |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2019 |
| International Standard Book Number | 9781470435509 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770276">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5770276</a> |
| Public note | Click to View |
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