线性支持向量分类机的平凡解  

Degenerate solution to linear support vector machine

作　　者：刘小茂[1] 全廷伟[1] 张钧[2] 

机构地区：[1]华中科技大学数学系,湖北武汉430074 [2]华中科技大学图像识别与人工智能研究所,湖北武汉430074

出　　处：《华中科技大学学报（自然科学版）》2007年第10期57-59,66,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60373090)

摘　　要：对二类分类问题,在线性可分或近似线性可分情况下,对线性支持向量分类机的平凡解进行了讨论,得出了解为平凡解的充要条件,说明了其几何意义,指出了避免出现这一现象的解决办法.该充要条件表明:对给定的训练集T,最优解是否为平凡解取决于训练集T的样本点在空间的分布位置,与惩罚参数C值的选取无关.一旦出现平凡解,线性支持向量分类机将会失效.为解决这一问题,可通过增加或减少训练集T中的样本点来实现.For binary classifying problem,we discuss the degeneracy of linear support vector machine（LSVM） which is applied for linearly separable or approximately linearly separable cases： derive necessary and sufficient conditions for the occurrence of degenerate solution and give their geometric explanations.The method to avoid its occurrence is also proposed.The necessary and sufficient conditions for the occurrence of degenerate solution indicate that for given training set,the optimal solution is whether degenerate one or not depends on the position of the training set T distributed in the space and is independent of the penalty parameter C.Whenever the optimal solution is degenerate,the linear support vector machine will be unavailable.To solve this problem,we may add or reduce some elements of the training set.

关 键 词：线性支持向量分类机 KKT条件 平凡解 线性可分 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O235[自动化与计算机技术—控制科学与工程]