This paper studies the problem of constructing a robust nonlinear classifier when the data set involves uncertainty and only the first- and second-order moments are known a priori. A distributionally robust chance-constrained kernel-free quadratic surface support vector machine (SVM) model is proposed using the moment information of the uncertain data. The proposed model is reformulated as a semidefinite programming problem and a second-order cone programming problem for efficient computations. A geometric interpretation of the proposed model is also provided. For commonly used data without prescribed uncertainty, a cluster-based data-driven approach is introduced to retrieve the hidden moment information that enables the proposed model for robust classification. Extensive computational experiments using synthetic and public benchmark data sets with or without uncertainty involved support the superior performance of the proposed model over other state-of-the-art SVM models, particularly when the data sets are massive and/or imbalanced.

中文翻译：

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分布稳健的机会约束无核二次曲面支持向量机

本文研究了当数据集涉及不确定性并且仅先验已知一阶和二阶矩时构造鲁棒非线性分类器的问题。利用不确定数据的矩信息，提出了一种分布鲁棒的机会约束无核二次曲面支持向量机（SVM）模型。所提出的模型被重新表述为半定规划问题和二阶锥规划问题，以实现高效计算。还提供了所提出模型的几何解释。对于没有规定不确定性的常用数据，引入基于集群的数据驱动方法来检索隐藏的矩信息，使所提出的模型能够进行鲁棒分类。使用包含或不包含不确定性的合成和公共基准数据集进行的广泛计算实验支持所提出的模型相对于其他最先进的 SVM 模型的优越性能，特别是当数据集庞大和/或不平衡时。