SVM最优分类面相对位置的修正

• 作 者: 周皓 李少洪
• 机 构: 北京航空航天大学电子信息工程学院,
• 出 处: 北京航空航天大学学报
• 发表日期: 2009年11期
• 关键词: 最优分类面 SVM 支持向量机 修正 计算复杂度 样本标准差 相对位置 思想框架 算法 间隔

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.

The condition that the sum of the interval of two kinds of functions is invariant is kept relaxed by relaxing the constraints of the class boundaries in the Support Vector Machines (SVM) at the equal intervals of the classification surface. The classification surface is derived from the support vector machine The new support vector machine with its dual form is exactly the same as the standard support vector machine, so as to further improve the support vector machine in theory.On the basis of this, a specific algorithm is proposed to make the class function interval proportional to the sample standard deviation - -Variance correction method to achieve the purpose of adjusting the relative position of the optimal classification surface according to the variance of samples.From the statistical sense, the variance correction method has improved the classification accuracy, but the amount of calculation increases little.