密度加权近似支持向量机

标准的近似支持向量机(PSVM)用求解正则化最小二乘问题代替了求解二次规划问题,它可以得到一个解析解,从而减少训练时间。但是标准的PSVM没有考虑数据集中正、负样本的分布情况,对所有的样本都赋予了相同的惩罚因子。而在实际问题中,数据集中样本的分布是不平衡的。针对此问题,在PSVM的基础上提出了一种基于密度加权的近似支持向量机(DPSVM),其先计算样本的密度指标,不同的样例有不同的密度信息,因此对不同的样例给予不同的惩罚因子,并将原始优化问题中的惩罚因子由数值变为一个对角矩阵。在UCI数据集上用这种方法进行了实验,并与SVM和PSVM方法进行了比较,结果表明,DPSVM在正负类样本分布不平衡的数据集上有较好的分类性能。

Density Weighted Proximal Support Vector Machine

The regularized least squares problem replaces the quadratic programming problem in the standard proximal support vector machines (PSVM). The proximal support vector machines has an analytic solution, so it reduces the training time. But the unbalanced data of positive and negative class is disregarded in the standard proximal support vector machines, and the same penalty factors are assigned to the all training samples. In practical problem, the distribution of positive and negative class is unbalance. Aiming at this problem, a density weighted proximal support vector machines(DPSVM) based on the support vector machines was presented, it is a modified proximal support vector machines algorithm. First calculated the density information of the different data, then according to the density information of the different sample, the different penalty factors were assigned to different training sample which has different density. The penalty values in the original problem of proximal support vector machines were transformed into a diagonal matrix.This method was used on UCI dataset, and compared with support vector machines and proximal support vector Machines methods. The experiment results indicate that the density weighted proximal support vector machines have a better efficiency classified performance in the unbalance data sets of positive and negative samples.