Title :
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
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;
Conference_Titel :
Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on
Conference_Location :
Guangzhou, China
Print_ISBN :
0-7803-9091-1
DOI :
10.1109/ICMLC.2005.1527680
