Generalized Mercer Kernels and Reproducing Kernel Banach Spaces (Memoirs of the American Mathematical Society) - Softcover

Yuesheng Xu (author) & Qi Ye (author)

Softcover

ISBN 10: 1470435500 ISBN 13: 9781470435509

Publisher: American Mathematical Society, 2019

Synopsis

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 $1\leq p\leq\infty$.

About this title

About the Author

Yuesheng Xu, Syracuse University, NY.

Qi Ye, South China Normal University, Guangzhou, China.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470435500
• ISBN 13: 9781470435509
• Binding: Paperback
• Number of pages: 122