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Geometrical Properties of Lifting-Up in the Nu Support Vector Machines Kazushi IKEDA Publication IEICE TRANSACTIONS on Information and Systems Vol.E89-D No.2 pp.847-852 Publication Date: 2006/02/01 Online ISSN: 1745-1361 DOI: 10.1093/ietisy/e89-d.2.847 Print ISSN: 0916-8532 Type of Manuscript: PAPER Category: Biocybernetics, Neurocomputing Keyword: support vector machines, lifting-up, homogeneous hyperplanes, Full Text: PDF(143.6KB)>>
Summary: Geometrical properties of the lifting-up technique in support vector machines (SVMs) are discussed here. In many applications, an SVM finds the optimal inhomogeneous separating hyperplane in terms of margins while some of the theoretical analyses on SVMs have treated only homogeneous hyperplanes for simplicity. Although they seem equivalent due to the so-called lifting-up technique, they differ in fact and the solution of the homogeneous SVM with lifting-up strongly depends on the parameter of lifting-up. It is also shown that the solution approaches that of the inhomogeneous SVM in the asymptotic case that the parameter goes to infinity. | ||||||||||
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