Journal
PATTERN RECOGNITION
Volume 44, Issue 3, Pages 607-614Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.patcog.2010.08.030
Keywords
Support vector machines; Nearest point problem; Reduced convex hulls; GSK algorithm; MDM algorithm
Funding
- Spain's TIN [2007-66862]
- Catedra UAM-IIC en Modelado y Prediccion
- Spanish Ministry of Education [AP2007-00142, AP2006-02285]
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The nearest point problem (NPP), i.e., finding the closest points between two disjoint convex hulls, has two classical solutions, the Gilbert-Schlesinger-Kozinec (GSK) and Mitchell-Dem'yanov-Malozemov (MDM) algorithms. When the convex hulls do intersect, NPP has to be stated in terms of reduced convex hulls (RCHs), made up of convex pattern combinations whose coefficients are bound by a mu < 1 value and that are disjoint for suitable it. The GSK and MDM methods have recently been extended to solve NPP for RCHs using the particular structure of the extreme points of a RCH. While effective, their reliance on extreme points may make them computationally costly, particularly when applied in a kernel setting. In this work we propose an alternative clipped extension of classical MDM that results in a simpler algorithm with the same classification accuracy than that of the extensions already mentioned, but also with a much faster numerical convergence. (C) 2010 Elsevier Ltd. All rights reserved.
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