Tian Yingjie, Ping Yuan
Research Center on Fictitious Economy & Data Science, Chinese Academy of Sciences, Beijing 100190, China.
Department of Computer Science and Technology, Xuchang University, Xuchang 461000, China; Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Neural Netw. 2014 Feb;50:166-74. doi: 10.1016/j.neunet.2013.11.014. Epub 2013 Nov 26.
Twin support vector machines (TWSVMs), as the representative nonparallel hyperplane classifiers, have shown the effectiveness over standard SVMs from some aspects. However, they still have some serious defects restricting their further study and real applications: (1) They have to compute and store the inverse matrices before training, it is intractable for many applications where data appear with a huge number of instances as well as features; (2) TWSVMs lost the sparseness by using a quadratic loss function making the proximal hyperplane close enough to the class itself. This paper proposes a Sparse Linear Nonparallel Support Vector Machine, termed as L1-NPSVM, to deal with large-scale data based on an efficient solver-dual coordinate descent (DCD) method. Both theoretical analysis and experiments indicate that our method is not only suitable for large scale problems, but also performs as good as TWSVMs and SVMs.
孪生支持向量机（TWSVMs）作为代表性的非平行超平面分类器，已在某些方面显示出优于标准支持向量机的有效性。然而，它们仍存在一些严重缺陷，限制了其进一步研究和实际应用：（1）在训练前必须计算和存储逆矩阵，对于许多具有大量实例和特征的数据应用来说难以处理；（2）TWSVMs通过使用二次损失函数失去了稀疏性，使得近端超平面足够接近类本身。本文提出了一种稀疏线性非平行支持向量机，称为L1-NPSVM，基于一种高效求解器——对偶坐标下降（DCD）方法来处理大规模数据。理论分析和实验均表明，我们的方法不仅适用于大规模问题，而且性能与TWSVMs和支持向量机相当。
