Large-Margin Classification in Banach Spaces

Ricky Der, Daniel Lee
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:91-98, 2007.

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 this Paper

BibTeX
@InProceedings{pmlr-v2-der07a, 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}, pages = {91--98}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/der07a/der07a.pdf}, url = {https://proceedings.mlr.press/v2/der07a.html}, 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.} }
Endnote
%0 Conference Paper %T Large-Margin Classification in Banach Spaces %A Ricky Der %A Daniel Lee %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-der07a %I PMLR %P 91--98 %U https://proceedings.mlr.press/v2/der07a.html %V 2 %X 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.
RIS
TY - CPAPER TI - Large-Margin Classification in Banach Spaces AU - Ricky Der AU - Daniel Lee BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-der07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 91 EP - 98 L1 - http://proceedings.mlr.press/v2/der07a/der07a.pdf UR - https://proceedings.mlr.press/v2/der07a.html AB - 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. ER -
APA
Der, R. & Lee, D.. (2007). Large-Margin Classification in Banach Spaces. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:91-98 Available from https://proceedings.mlr.press/v2/der07a.html.

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