基于相似压缩的近似线性SVM

Approximate Linear SVM Based on Similitude Squeezing

为了解决模式识别中的近似线性可分问题,提出了一种新的近似线性支持向量机(SVM).首先对近似线性分类中的训练集所形成的两类凸壳进行了相似压缩,使压缩后的凸壳线性可分;基于压缩后线性可分的凸壳,再用平分最近点和最大间隔法求出最优的分划超平面.然后再通过求解最大间隔法的对偶问题,得到基于相似压缩的近似线性SVM.最后,从理论和实证分析两个方面,将该方法与线性可分SVM及推广的平分最近点法进行了对比分析,说明了该方法的优越性与合理性.

To solve the approximate linearly separable problem in pattern recognition,a new approximate linear Support Vector Machine（SVM） is presented.First,the two convex hulls from the training set of approximate linear classification are similarly squeezed into the linearly separable ones,and based on the two similarly squeezed linearly separable convex hulls,an optimal separating hyperplane is figured out by using the method of halving the nearest points and the maximal margin method.Then,the approximately linear SVM is obtained by solving the dual problem of maximal margin method.Finally,analysis is made from both theoretical and empirical aspects to compare the proposed new SVM,the known linear SVMs and the generalized method of halving the nearest points,and the advantages and rationality of the new SVM are demonstrated.