Density Weighted Proximal Support Vector Machine
密度加权近似支持向量机

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.