A Novel Classification Method Based on Hypersurface

The main idea of the support vector machine (SVM) classification approach is mapping the data into higher-dimensional linear space where the data can be separated by hyperplane. Based on the Jordan curve theory, a general nonlinear classification method by the use of hypersurface is proposed in this paper. The separating hypersurface is directly used to classify the data according to whether the number of intersections with the radial is odd or even. In contrast to the SVM approach, the proposed approach has no need for mapping from lower-dimensional space to higher-dimensional space. Furthermore, the approach does not use kernel functions and it can directly solve the nonlinear classification problem via the hypersurface. Numerical experiments showed that the proposed approach can efficiently and accurately solve the classification problems with a large amount of data @ 2003 Elsevier Ltd. All rights reserved. Keywords-support vector machine, Hypersurface, Jordan curve theory, Statistical learnmg theory, VC dimension.