The Support Vector Machine (SVM) is one of the most popular classification methods in the machine learning literature. Binary SVM methods have been extensively studied, and have achieved many successes in various disciplines. However, generalization to Multicategory SVM (MSVM) methods can be very challenging. Many existing methods estimate k functions for k classes with an explicit sum-to-zero constraint. It was shown recently that such a formulation can be suboptimal. Moreover, many existing MSVMs are not Fisher consistent, or do not take into account the effect of outliers. In this paper, we focus on classification in the angle-based framework, which is free of the explicit sum-to-zero constraint, hence more efficient, and propose two robust MSVM methods using truncated hinge loss functions. We show that our new classifiers can enjoy Fisher consistency, and simultaneously alleviate the impact of outliers to achieve more stable classification performance. To implement our proposed classifiers, we employ the difference convex algorithm (DCA) for efficient computation. Theoretical and numerical results obtained indicate that for problems with potential outliers, our robust angle-based MSVMs can be very competitive among existing methods.

中文翻译：

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使用差分凸算法的鲁棒多类别支持向量机。

支持向量机（SVM）是机器学习文献中最受欢迎的分类方法之一。二进制SVM方法已经得到了广泛的研究，并在各个领域取得了许多成功。但是，将通用化为多类别SVM（MSVM）方法可能非常困难。许多现有方法都使用明确的零和约束来估计k个类的k个函数。最近显示，这种制剂可能不是最佳的。此外，许多现有的MSVM并非费雪一致的，或者没有考虑离群值的影响。在本文中，我们专注于基于角度的框架中的分类，该分类不受显式的零和约束，因此效率更高，并提出了两种使用截断的铰链损失函数的鲁棒MSVM方法。我们表明，我们的新分类器可以享受Fisher一致性，同时减轻离群值的影响，以实现更稳定的分类性能。为了实现我们提出的分类器，我们采用差分凸算法（DCA）进行有效的计算。理论和数值结果表明，对于存在潜在异常值的问题，基于角度的稳健MSVM在现有方法中可能具有很高的竞争力。