title: Reinforced Angle-based Multicategory Support Vector Machines.
abstract: 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 ofkclassification functions for ak-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 withk- 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.
authors.affiliation: Department of Statistics and Actuarial Science, University of Waterloo.
authors.forename: Chong
authors.initials: C
authors.lastname: Zhang
authors.affiliation: Department of Statistics and Operations Research, University of North Carolina at Chapel Hill; Department of Genetics, University of North Carolina at Chapel Hill; Department of Biostatistics, University of North Carolina at Chapel Hill.
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Department of Mathematics, City University of Hong Kong.
authors.forename: Junhui
authors.initials: J
authors.lastname: Wang
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
keywords: Coordinate Descent Algorithm; Fisher Consistency; Multicategory Classification; Quadratic Programming; Reproducing Kernel Hilbert Space