Large-Margin Classification in Banach Spaces
Abstract
We propose a framework for dealing with binary hard-margin classification in Banach spaces, centering on the use of a supporting semi-inner-product (s.i.p.) taking the place of an inner-product in Hilbert spaces. The theory of semi-inner-product spaces allows for a geometric, Hilbert-like formulation of the problems, and we show that a surprising number of results from the Euclidean case can be appropriately generalised. These include the Representer theorem, convexity of the associated optimization programs, and even, for a particular class of Banach spaces, a “kernel trick” for non-linear classification.
Cite
Text
Der and Lee. "Large-Margin Classification in Banach Spaces." Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, 2007.Markdown
[Der and Lee. "Large-Margin Classification in Banach Spaces." Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, 2007.](https://mlanthology.org/aistats/2007/der2007aistats-largemargin/)BibTeX
@inproceedings{der2007aistats-largemargin,
title = {{Large-Margin Classification in Banach Spaces}},
author = {Der, Ricky and Lee, Daniel},
booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics},
year = {2007},
pages = {91-98},
volume = {2},
url = {https://mlanthology.org/aistats/2007/der2007aistats-largemargin/}
}