SVM最优分类面相对位置的修正

Relative position modification of SVM's optimal hyperplane

通过放宽标准支持向量机(SVM,Support Vector Machines)中类别边界至分类面等间隔的约束,保持两类函数间隔之和不变的条件,在支持向量机思想框架下得出分类面依样本分布进行调整的新型支持向量机,其对偶形式与标准支持向量机完全相同,从而在理论上进一步完善了支持向量机.在此基础上,提出使类别的函数间隔正比于样本标准差的具体算法——方差修正法,达到最优分类面的相对位置依样本方差而调整之目的.从统计意义上来说,方差修正法在分类精度上有所提高,但计算量增加不多.

Through releasing the equal-margin constraint in the standard support vector machines（SVM）,keeping the sum of the binary-class function margins,a new SVM was gotten within the framework of SVM.The separating hyperplane of the new SVM can be adjusted as per the distribution of the binary-class samples,and its dual express is same as the standard SVM.Thus,the SVM was further improved theoretically.On the basis of the new SVM,a concrete algorithm,variance modification algorithm,was proposed.In the variance modification algorithm,the binary-class margins are in proportion to the standard deviation of binary-class samples.The goal of adjusting the optimal separating hyperplane as per sample＇s variance is attained through the variance modification algorithm.Statistically,errors are reduced through the variance modification algorithm,while the computational complexity is not increased much.