Reproducing Kernel Banach Spaces for Machine Learning
Abstract
We introduce the notion of reproducing kernel Banach spaces (RKBS) and study special semi-inner-product RKBS by making use of semi-inner-products and the duality mapping. Properties of an RKBS and its reproducing kernel are investigated. As applications, we develop in the framework of RKBS standard learning schemes including minimal norm interpolation, regularization network, support vector machines, and kernel principal component analysis. In particular, existence, uniqueness and representer theorems are established.
Cite
Text
Zhang et al. "Reproducing Kernel Banach Spaces for Machine Learning." Journal of Machine Learning Research, 2009.Markdown
[Zhang et al. "Reproducing Kernel Banach Spaces for Machine Learning." Journal of Machine Learning Research, 2009.](https://mlanthology.org/jmlr/2009/zhang2009jmlr-reproducing/)BibTeX
@article{zhang2009jmlr-reproducing,
title = {{Reproducing Kernel Banach Spaces for Machine Learning}},
author = {Zhang, Haizhang and Xu, Yuesheng and Zhang, Jun},
journal = {Journal of Machine Learning Research},
year = {2009},
pages = {2741-2775},
volume = {10},
url = {https://mlanthology.org/jmlr/2009/zhang2009jmlr-reproducing/}
}