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Geometric algorithms for parametric-margin ν-support vector machine
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DOI：10.1016/j.neucom.2012.06.026.png)
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Abstract
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The parametric-margin nu-support vector machine (par-nu-SVM) is a useful classifier in many cases, especially when the noise is heteroscedastic. In this paper, the geometric interpretation for the par-nu-SVM is described, which is equivalent to finding a couple of points in two disjoint mu-reduced convex hulls (mu-RCHs) by simultaneously minimizing the square distance and maximizing the square norm of their sum with a weight factor 1/(c nu) given by users. Motivated by the Gilbert-Schlesinger-Kozinec (GSK) and Mitchell-Dem'yanov-Malozemov (MDM) algorithms, two geometric algorithms, called the parametric mu-GSK (par-mu-GSK) and parametric mu-MDM (par-mu-MDM) algorithms, are introduced to solve the par-nu-SVM. Computational results on several synthetic as well as benchmark datasets demonstrate the significant performance of the proposed algorithms in terms of both kernel operations and classification accuracy. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.
Keywords:
Support vector machine
Parametric-margin
Nearest point problem
Reduced convex hull
Geometric algorithm
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6.5
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