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IEICE Transactions on Information and Systems 2006 E89-D(2):847-852; doi:10.1093/ietisy/e89-d.2.847
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Copyright © 2006 The Institute of Electronics, Information and Communication Engineers

Regular Section -- Papers -- Biocybernetics, Neurocomputing

Geometrical Properties of Lifting-Up in the Nu Support Vector Machines*

Kazushi IKEDA1

1 The author is with Kyoto University, Kyoto-shi, 606–8501 Japan. E-mail: kazushi{at}i.kyoto-u.ac.jp

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.

Key Words: support vector machines, lifting-up, homogeneous hyperplanes

Manuscript received April 14, 2005. Manuscript revised September 6, 2005.

* This study is supported in part by Grant-in-Aid for Scientific Research (14084210, 15700130) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.


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