VC-dimension on manifolds: a first approach

被引：1

作者：

Ferri, Massimo ^{[1
,2
]}

Frosini, Patrizio ^{[1
,2
]}

机构：

[1] ARCES, I-40126 Bologna, Italy

[2] Dept Math, I-40126 Bologna, Italy

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2008年 / 31卷 / 05期

关键词：

statistical learning; covering projection; Vapnik-Chervonenkis-dimension; Morse function;

D O I：

10.1002/mma.927

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Vapnik-Chervonenkis-dimension is an index of the capacity of a learning machine. It has been computed in several cases, but always in a Euclidean context. This paper extends the notion to classifiers acting in the more general environment of a manifold. General properties are proved, and some examples of simple classifiers on elementary manifolds are given. A large part of the research is directed toward a still open problem on product manifolds. Copyright (C) 2007 John Wiley & Sons, Ltd.

引用

页码：589 / 605

页数：17