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

Kazushi IKEDA

doi:10.1093/ietisy/e89-d.2.847

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

Kazushi IKEDA

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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.

Publication: IEICE TRANSACTIONS on Information Vol.E89-D No.2 pp.847-852

Publication Date: 2006/02/01

Publicized

Online ISSN: 1745-1361

DOI: 10.1093/ietisy/e89-d.2.847

Type of Manuscript: PAPER

Category: Biocybernetics, Neurocomputing

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Kazushi IKEDA, "Geometrical Properties of Lifting-Up in the Nu Support Vector Machines" in IEICE TRANSACTIONS on Information, vol. E89-D, no. 2, pp. 847-852, February 2006, doi: 10.1093/ietisy/e89-d.2.847.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/information/10.1093/ietisy/e89-d.2.847/_p

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@ARTICLE{e89-d_2_847,
author={Kazushi IKEDA, },
journal={IEICE TRANSACTIONS on Information},
title={Geometrical Properties of Lifting-Up in the Nu Support Vector Machines},
year={2006},
volume={E89-D},
number={2},
pages={847-852},
abstract={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.},
keywords={},
doi={10.1093/ietisy/e89-d.2.847},
ISSN={1745-1361},
month={February},}

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TY - JOUR
TI - Geometrical Properties of Lifting-Up in the Nu Support Vector Machines
T2 - IEICE TRANSACTIONS on Information
SP - 847
EP - 852
AU - Kazushi IKEDA
PY - 2006
DO - 10.1093/ietisy/e89-d.2.847
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E89-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2006
AB - 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.
ER -