基于最小流形类内离散度的支持向量机

摘要

Support vector machine (SVM)is one of the most popular classification methods and widely used in practice.But with the development of application,it encounters a problem which seriously limits the classification efficiency:it only focuses on the margin between classes,but ignores the class distributions.In order to solve the above problem,this paper proposed min-imum class variance support vector machine (MCVSVM)by Zafeiriou and considered boundary information and distribution characteristics and therefore its classification efficiency was much better than SVM.The local characteristics of each class was quite important but it was regrettable that it was neglected by both SVM and MCVSVM.In view of this,this paper proposed support vector machine based on minimum manifold-based within-class scatter (SVM-M2 WCS ).The theoretical and experi-mental analysis shows the effectiveness of our proposed methods.%尽管经典分类方法支持向量机SVM在各领域广泛应用，但其在分类决策时仅关注类间间隔而忽视类内分布，因而分类能力有限。鉴于此，Zafeiriou等人提出最小类方差支持向量机MCVSVM，该方法建立在支持向量机和线性判别分析的基础上，在进行分类决策时同时考虑各类的边界信息和分布特征，因而较之SVM具有更优的泛化能力。但上述两种方法均忽略了样本的局部特征。基于上述分析，在流形判别分析的基础上提出基于最小流形类内离散度的支持向量机SVM-M2 WCS。该方法在建立最优分类面时，不仅考虑各类的边界信息和分布特征，而且还保持了各类的局部流形结构。经理论分析可得该方法在一定条件下与SVM和MCVSVM等价，这表明SVM-M2 WCS较之SVM和MCVSVM具有更优的泛化能力。人工数据集及标准数据集上的比较实验表明SVM-M2 WCS的有效性。