Separating two classes of samples using support vectors in a convex hull

Author

Wu, Cong-Xin ; Yeung, Daniel S. ; Tsang, Eric C C

Author_Institution

Dept. of Math., Harbin Inst. of Technol., China

Volume

7

fYear

2005

fDate

18-21 Aug. 2005

Firstpage

4233

Abstract

In this paper, we present the necessary and sufficient conditions of two finite classes of samples that can be separated by a hyperplane in terms of support vectors which are just the vertices of a convex hull of each class of samples. We also extend the calculating formula of the margin of an optimal separating hyperplane to some cases of the classes of infinite samples in Hilbert space. These results are the generalization and improvement of the corresponding results for the theory of SVM in Euclidian space.

Keywords

Hilbert spaces; computational geometry; pattern classification; set theory; support vector machines; Euclidian space; Hilbert space; classification; convex hull vertices; optimal separating hyperplane; sample class separation; support vectors; Cybernetics; Data mining; Geometry; Hilbert space; Machine learning; Mathematics; Pattern recognition; Sufficient conditions; Support vector machine classification; Support vector machines; Classification; Compactness; Convex hull; Hilbert space; Margin; Separating hyperplane; Vertex;

fLanguage

English

Publisher

ieee

Conference_Titel

Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on

Conference_Location

Guangzhou, China

Print_ISBN

0-7803-9091-1

Type

conf

DOI

10.1109/ICMLC.2005.1527680

Filename

1527680