Reinforced Angle-Based Multicategory Support Vector Machines

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)806-825
Journal / PublicationJournal of Computational and Graphical Statistics
Issue number3
Publication statusPublished - 2 Jul 2016


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 article, 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.

Research Area(s)

  • Coordinate descent algorithm, Fisher consistency, Multicategory classification, Quadratic programming, Reproducing kernel Hilbert space