With the introduction of the regularization term in the formulation of the well-known twin support vector machine (TWSVM) for classification, twin bounded support vector machine (TBSVM) method was proposed recently as an improved version by implementing the structural risk minimization principle. However, TBSVM employs hinge loss function and it is sensitive to noise and unstable to re-sampling. Since the pinball loss function related to quantile distance enjoys noise insensitivity property, a novel TBSVM method with squared pinball loss function for classification is proposed. The noise insensitivity and scatter minimization properties are discussed. Our formulation is further simplified as a pair of unconstrained strongly convex minimization problems in the dual space free of matrix inversion terms and having only m variables where m is the number of training examples. As opposed to TWSVM and TBSVM wherein approximate kernel generated surfaces are constructed, kernel trick is applied directly in our formulation and thereby elegant formulation as in the classical support vector machine (SVM) is achieved. Numerical experiments performed on a synthetic and thirteen benchmark datasets with noise where better or comparable generalization performance with faster learning speed by the proposed method confirms its suitability and applicability to problems of interest.

随着正则化项在著名的双支持向量机（TWSVM）分类中的引入，最近提出了双边界支持向量机（TBSVM）方法，通过实现结构风险最小化原理进行了改进。但是，TBSVM具有铰链损耗功能，并且对噪声敏感并且对重新采样不稳定。由于与分位数距离有关的弹球损失函数具有噪声不敏感特性，因此提出了一种新的具有平方弹球损失函数的TBSVM方法进行分类。讨论了噪声不敏感度和散射最小化属性。我们的公式进一步简化为一对无约束的强凸最小化问题在没有矩阵求逆项的对偶空间中，仅具有m个变量，其中m是训练示例的数量。与构造近似的内核生成表面的TWSVM和TBSVM相反，将内核技巧直接应用到我们的公式中，从而可以实现经典支持向量机（SVM）中的优雅公式。在具有噪声的合成和13个基准数据集上进行的数值实验表明，所提出的方法具有更好的或可比较的泛化性能，并且学习速度更快，这证实了其对感兴趣的问题的适用性和适用性。