A family of norm-based least squares support vector machines (LSSVMs) is the effective statistical learning tool and has attracted considerable attentions. However, there are two critical problems: (1) LSSVM is ill-conditioned or singular when the sample size is much less than feature number and thus causes over-fitting for small sample size (SSS) problem, while other norm-based LSSVMs own slower training speed and cannot deal with large scale data. (2) Norm-based LSSVMs pay less attention to the edge points that are important for learning the final classifier. To overcome the above drawbacks, by replacing \( L_{2}\text{-}norm \) with \( L_{\infty }\text{-}norm \) in empirical loss, we construct a robust classifier, named \( L_{\infty }\text{-}LSSVM \) in short. After adjustment, \( L_{\infty }\text{-}LSSVM \) can detect edge points effectively and enhances the capability of the robustness and the generalization. Also, inspired by the idea of sequential minimal optimization (SMO), we design a novel SMO-typed iterative algorithm. The new algorithm not only guarantees the convergence of optimum solution in theory, but also owns the lower computational time and storage space when data size is large. Finally, extensive numerical experiments validate the above opinions again on four groups of artificial data, Non-i.i.d data: fault detection of railway turnout, four SSS datasets, two types of massive datasets and six benchmark datasets.

基于范数的最小二乘支持向量机（LSSVM）系列是有效的统计学习工具，受到了广泛的关注。但是，存在两个关键问题：（1）当样本量远小于特征数时，LSSVM处于病态或奇异状态，从而导致对小样本量（SSS）问题的过度拟合，而其他基于规范的LSSVM拥有训练速度较慢，无法处理大规模数据。（2）基于范数的LSSVM较少关注对学习最终分类器至关重要的边缘点。为了克服上述缺点，在经验损失中，用\（L _ {\ infty} \ text {-} norm \）替换\（L_ {2} \ text {-} norm \），我们构造了一个健壮的分类器，命名为\ （L _ {\ infty} \ text {-} LSSVM \）简而言之。调整后，\（L _ {\ infty} \ text {-} LSSVM \）可以有效地检测边缘点，并增强了鲁棒性和泛化能力。同样，受顺序最小优化（SMO）的启发，我们设计了一种新颖的SMO型迭代算法。新算法不仅在理论上保证了最优解的收敛性，而且在数据量大时具有较低的计算时间和存储空间。最后，大量的数值实验再次验证了上述四组人工数据，非空袭数据的观点：铁路道岔的故障检测，四个SSS数据集，两种类型的海量数据集和六个基准数据集。