L无穷范数软间隔支持向量机分类  

Soft margin support vector classification by L-infinity norm

作　　者：罗林开[1] 张晓东[1] 

机构地区：[1]厦门大学自动化系,厦门361005

出　　处：《东南大学学报（自然科学版）》2010年第S1期234-237,共4页Journal of Southeast University：Natural Science Edition

基　　金：福建省自然科学基金资助项目(2008J0033)

摘　　要：为了使支持向量机具有更好的泛化性能,利用松弛变量的无穷范数度量经验风险,根据结构风险最小化原则,提出了L无穷范数软间隔支持向量机分类模型(L-infinity-SVC).利用La-grange对偶理论,导出其对偶问题,给出了原问题解与对偶问题解之间的关系式以及分类超平面的计算公式.然后,利用基准数据集,在相同的训练集和测试集上对L-infinity-SVC,1-范数度量的支持向量分类(L1-SVC)和2-范数度量的支持向量分类(L2-SVC)进行了比较实验.实验结果显示,L-infinity-SVC的测试集准确率与训练集准确率的相对误差均小于L1-SVC与L2-SVC,且L-infinity-SVC的测试准确率均略高于L1-SVC和L2-SVC,表明L-infinity-SVC可取得更好的泛化性能,是一个可与L1-SVC和L2-SVC相竞争的模型.To obtain a better generalization performance,an L-infinity soft margin support vector classification model ( L-infinity-SVC) is proposed by the principle of structural risk minimization and the empirical risk measured with infinite norm of slack variables. According to the Lagrange duality theory,the dual problem of the L-infinity-SVC is deduced. The relationship between the solution of the original problem and that of the dual problem and the calculation formula of the classification separating hyperplane are presented. Then,the comparative experiments of the L-infinity-SVC,the L1-SVC and the L2-SVC on benchmark datasets with the same training sets and test sets are carried out. The experimental results show that the relative error of accuracy of the test sets and the training sets in the L-infinity-SVC is lower than those in the L1-SVC and the L2-SVC,and the accuracy rate on the test sets in the L-infinity-SVC is slightly higher. Therefore,the L-infinity-SVC has a better generalization performance,indicting it is competitive with the L1-SVC and the L2-SVC.

关 键 词：L无穷范数 支持向量机 无穷范数 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]