基于数据深度的支撑向量估计

针对支撑向量机分类问题,提出了利用空间秩深度估计两类样本潜在支撑向量的方法。首先计算出样本在相对本类和相对于异类的深度,然后取其比值作为相对深度。注意到样本相对深度在交界面位置较大的特性,我们用相对深度估计样本中的潜在支撑向量。对非线性分类问题,我们给出了特征空间下的深度计算公式,拓宽了算法的适用范围。利用潜在支撑向量信息,我们不仅可以除去大量的计算冗余样本,而且可以利用边界信息通过修正核提高支撑向量机的分类性能。

Abstract：

A method was proposed to estimate the potential support vectors （SVs） in advance based on spatial rank depth （SRD） in binary classification by support vector machine （SVM）. Noting that the ratio of relative-class data depth to inner-class data depth is extra large in the interface of the two datasets,the relative depth was used to estimate the support vectors in the samples. According to the nonlinear classification,the spatial rank depth in the feature space was discussed. By estimating the SVs in advance,the computation not only could be reduced by removing the redundant data while keeping the precision,but also the performance of SVM could be improved by the revised kernel method using the interface information.

Estimation for Support Vectors by Data Depth

A method was proposed to estimate the potential support vectors （SVs） in advance based on spatial rank depth （SRD） in binary classification by support vector machine （SVM）. Noting that the ratio of relative-class data depth to inner-class data depth is extra large in the interface of the two datasets,the relative depth was used to estimate the support vectors in the samples. According to the nonlinear classification,the spatial rank depth in the feature space was discussed. By estimating the SVs in advance,the computation not only could be reduced by removing the redundant data while keeping the precision,but also the performance of SVM could be improved by the revised kernel method using the interface information.