ML Anthology

On the VC Dimension of Bounded Margin Classifiers

Don R. Hush, Clint Scovel
MLJ 2001 pp. 33-44
doi:10.1023/A:1010971905232 /mlj/2001/hush2001mlj-vc/

Abstract

In this paper we prove a result that is fundamental to the generalization properties of Vapnik's support vector machines and other large margin classifiers. In particular, we prove that the minimum margin over all dichotomies of k ≤ n + 1 points inside a unit ball in R n is maximized when the points form a regular simplex on the unit sphere. We also provide an alternative proof directly in the framework of level fat shattering.

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Text

Hush and Scovel. "On the VC Dimension of Bounded Margin Classifiers." Machine Learning, 2001. doi:10.1023/A:1010971905232

Markdown

[Hush and Scovel. "On the VC Dimension of Bounded Margin Classifiers." Machine Learning, 2001.](https://mlanthology.org/mlj/2001/hush2001mlj-vc/) doi:10.1023/A:1010971905232

BibTeX

@article{hush2001mlj-vc,
  title     = {{On the VC Dimension of Bounded Margin Classifiers}},
  author    = {Hush, Don R. and Scovel, Clint},
  journal   = {Machine Learning},
  year      = {2001},
  pages     = {33-44},
  doi       = {10.1023/A:1010971905232},
  volume    = {45},
  url       = {https://mlanthology.org/mlj/2001/hush2001mlj-vc/}
}