支持向量机平凡解判别与修正的新方法

A new method for discrimination and modification of null solutions in support vector machines

针对二类分类问题,提出一种新的线性支持向量机(SVM)产生平凡解的判别与修正方法,证明如下SVM平凡解判别定理:SVM最优解是平凡解的充要条件是在样本空间的任意方向上,正负类训练样本的分布满足某种不等式关系,该不等式与正负类训练样本各自的惩罚因子C+、C-有关,与公共的惩罚因子C无关。在以上判别定理的基础上,通过筛选训练样本点及各自的惩罚因子来修正SVM优化求解过程,为有效避免SVM平凡解的产生提供理论依据和技术手段。仿真计算实例表明该方法有效。

For binary classification problems, a new method for discrimination and modification of null solutions in linear support vector machines （SVMs） was proposed. The following theorems for discrimination of null solutions in SVMs were proved： The necessary and sufficient conditions for the optimal solution of SVMs being a null solution are that for a given training set, the distribution of the positive and negative samples must satisfy an inequality which is related to the respective penalty parameters C＋, C- of the two classes, and is independent of the shared penalty parameter C. Based on the above results, a modification method for null solutions in SVMs was presented by selecting samples in the training set, and adjusting the values of penalty parameters, which provides theoretical support and technique method for avoiding generating null solutions in SVMs. Computational examples illustrate the effectiveness of the proposed methods.