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.

中文翻译：

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强化的基于角度的多类别支持向量机


支持向量机（SVM）是一种非常流行的分类工具，有许多成功的应用。它最初是为具有理想理论性质的二元问题而设计的。尽管文献中存在各种多类别 SVM (MSVM) 扩展，但仍然存在一些挑战。特别是，大多数现有的 MSVM 对 k 类问题使用 k 个分类函数，并且相应的优化问题通常由现有的二次规划求解器处理。在本文中，我们提出了一组新的 MSVM，即增强型基于角度的 MSVM（RAMSVM），直接使用具有 k − 1 个函数的基于角度的预测规则。我们证明 RAMSVM 可以享受 Fisher 一致性。此外，我们表明 RAMSVM 可以在其对偶问题上使用非常有效的坐标下降算法来实现。数值实验表明，我们的方法在计算速度以及分类预测性能方面具有很强的竞争力。本文的补充材料可在线获取。