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

Xu, Yuesheng/ Ye, Qi

American Mathematical Society（2019/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 122 p.
• 言語 ENG
• 商品コード 9781470435509
• DDC分類 515.732

Full Description

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 $1\leq p\leq\infty$.

Contents

Introduction
Reproducing Kernel Banach Spaces
Generalized Mercer Kernels
Positive Definite Kernels
Support Vector Machines
Concluding Remarks
Acknowledgments
Index
Bibliography.