The geometric relationship between Core Vector Machine and Support Vector Machine
Liang Chang · 2008
Core vector machine (CVM) is an efficient kernel method for large data classification. It has prominent advantages in dealing with large data sets in high-dimensional space. This paper presents a novel geometric framework between CVM and the traditional support vector machine (SVM). We proved theoretically that: (1) In one-class classification, non-training examples on the surface of the exact minimum enclosing ball (MEB) in CVM belong to the optimal separating hyperplane in SVM; (2) In one-class classification, training examples on the surface of the exact MEB in CVM correspond to the support vectors in SVM; (3) In two-class classification, non-training examples on the surface of the exact MEB in CVM belong to the bounding hyperplanes in SVM; (4) In two-class classification, training examples on the surface of the exact MEB in CVM correspond to the support vectors in SVM. Geometric interpretations for points on the (1 + epsiv)-approximate MEB in CVM are presented as well. It is believed that the obtained geometric relationship will be helpful in analyzing CVM and inspiring new classification algorithms.