摘要
【目的】针对二分类问题,构造了一种新的基于L1-范数的v-双子限定支持向量机(L1-vTBSVM)。【方法】类似于v-双子限定支持向量机(v-TBSVM),L1-vTBSVM确定两个非平行超平面,使得它们更接近于各自的类,并且与另一个类至少有ρ的距离。在L1-vTBSVM中,由于用L1-范数替代了L2-范数,则相较于v-TBSVM,所提模型产生了不同的对偶问题。【结果】在求解对偶问题时避免了昂贵的矩阵逆运算,更重要的是,L1-vTBSVM可以抑制离群值的负面影响,从而提高模型的鲁棒性。因此,改进的模型在处理大规模问题时更有效,且具有更好的泛化能力。【结论】在6个基准数据集上进行了数值实验,验证了该算法在线性、非线性和加入噪声情况下的有效性。
[Purposes]To solve the binary classification problem,a newv-twin bounded support vector machine(L1-vTBSVM)based on L1-norm is proposed.[Methods]Similar to v-TBSVM,L1-vTBSVM determines two non-parallel hyperplanes,making them closer to their respective classes,and at least with a distance of ρ from another class.In L1-vTBSVM,the L2-norm is replaced by the L1-norm,compared to v-TBSVM,the proposed model produces different dual problem.[Findings]The costly inverse matrix operation is avoided when solving the dual problem.More importantly,L1-vTBSVM can suppress the negative influence of outliers and improve the robustness of the model.Therefore,the model proposed is more effective in dealing with large-scale problems and has better generalization ability.[Conclusions]Numerical experiments are carried out on six benchmark datasets to verify the effectiveness of the algorithm under linear,nonlinear and noise-added conditions.
作者
廖均淋
白富生
马龙
LIAO Junlin;BAI Fusheng;MA Long(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
2020年第2期1-11,共11页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.11871128)。
