ABSTRACT Twin K-class support vector classification (TKSVC) adopts ‘One-vs.-One-vs.-Rest’ structure to utilise all the samples to increase the prediction accuracy. However, TKSVC is sensitive to noises or outliers due to the use of the Hinge loss function. To reduce the negative influence of outliers, in this paper, we propose a more robust algorithm termed as Ramp loss for twin K-class support vector classification (Ramp-TKSVC) where we use the Ramp loss function to substitute the Hinge loss function in TKSVC. Because the Ramp-TKSVC is a non-differentiable non-convex optimisation problem, we adopt Concave–Convex Procedure (CCCP) to solve it. To overcome the drawbacks of conventional multi-classification methodologies, the TKSVC is utilised as a core of our Ramp-TKSVC. In the Ramp-TKSVC, the outliers are prevented from becoming support vectors, thus they are not involved in the construction of hyperplanes, making the Ramp-TKSVC more robust. Besides, the Ramp-TKSVC is sparser than the TKSVC. To verify the validity of our Ramp-TKSVC, we conduct experiments on 12 benchmark datasets in both linear and nonlinear cases. The experimental results indicate that our algorithm outperforms the other five compared algorithms.

中文翻译：

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双多类支持向量分类的斜坡损失

摘要 Twin K 类支持向量分类（TKSVC）采用'One-vs.-One-vs.-Rest' 结构来利用所有样本来提高预测精度。然而，由于使用了铰链损失函数，TKSVC 对噪声或异常值很敏感。为了减少异常值的负面影响，在本文中，我们提出了一种更稳健的算法，称为双 K 类支持向量分类的斜坡损失 (Ramp-TKSVC)，其中我们使用斜坡损失函数代替 TKSVC 中的铰链损失函数. 由于 Ramp-TKSVC 是一个不可微的非凸优化问题，我们采用 Concave-Convex Procedure (CCCP) 来解决它。为了克服传统多分类方法的缺点，TKSVC 被用作我们 Ramp-TKSVC 的核心。在 Ramp-TKSVC 中，异常值被阻止成为支持向量，因此它们不参与超平面的构建，使 Ramp-TKSVC 更加健壮。此外，Ramp-TKSVC 比 TKSVC 更稀疏。为了验证我们的 Ramp-TKSVC 的有效性，我们在线性和非线性情况下对 12 个基准数据集进行了实验。实验结果表明，我们的算法优于其他五种比较算法。