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Reinforced Angle-based Multicategory Support Vector Machines

1Department of Statistics and Actuarial Science, University of Waterloo.
2Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, NC, USA.
3Department of Mathematics, City University of Hong Kong.
4Department of Biostatistics, University of North Carolina at Chapel Hill, NC, USA.
Publication Date:
J Comput Graph Stat
Volume Number:
Issue Number:
J Comput Graph Stat. 2016 Aug;25(3):806-25.
PubMed ID:
Coordinate Descent Algorithm, Fisher Consistency, Multicategory Classification, Quadratic Programming, Reproducing Kernel Hilbert Space
Appears in Collections:
U54 EB005149/EB/NIBIB NIH HHS/United States
R01 CA149569/CA/NCI NIH HHS/United States
P01 CA142538/CA/NCI NIH HHS/United States
UL1 RR025747/RR/NCRR NIH HHS/United States
R01 MH086633/MH/NIMH NIH HHS/United States
Generated Citation:
Zhang C., Liu Y., Wang J., Zhu H. Reinforced Angle-based Multicategory Support Vector Machines. J Comput Graph Stat. 2016 Aug;25(3):806-25. PMID: 27891045. PMCID: PMC5120762.
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The Support Vector Machine (SVM) is a very popular classification tool with many successful applications. It was originally designed for binary problems with desirable theoretical properties. Although there exist various Multicategory SVM (MSVM) extensions in the literature, some challenges remain. In particular, most existing MSVMs make use of k classification functions for a k-class problem, and the corresponding optimization problems are typically handled by existing quadratic programming solvers. In this paper, we propose a new group of MSVMs, namely the Reinforced Angle-based MSVMs (RAMSVMs), using an angle-based prediction rule with k − 1 functions directly. We prove that RAMSVMs can enjoy Fisher consistency. Moreover, we show that the RAMSVM can be implemented using the very efficient coordinate descent algorithm on its dual problem. Numerical experiments demonstrate that our method is highly competitive in terms of computational speed, as well as classification prediction performance. Supplemental materials for the article are available online.