一种基于密度加权的最小二乘支持向量机稀疏化算法

Density Weighted Pruning Method for Sparse Least Squares Support Vector Machines

针对最小二乘支持向量机失去标准支持向量机稀疏特性的问题,提出了一种基于密度加权的稀疏化算法.首先计算样本的密度信息,对样本估计误差进行密度加权获得该样本对模型的可能贡献度;然后选取具有最大可能贡献度的样本作为支持向量,同时对支持向量样本邻域内的其他样本密度信息进行削减,从而避免相似样本被选中为支持向量;再选择剩余样本中具有最大可能贡献度的样本添加到支持向量集中,直到模型性能满足要求.仿真和实际应用表明,与Suykens提出的标准稀疏化算法相比,所提出的算法能有效剔除冗余支持向量,具有更好的稀疏性和鲁棒性.

For lack of sparseness characteristic in support vector machines （SVM） by least squares solution （LSSVM）, a density weighted pruning algorithm to improve the sparseness of the LSSVM regression model is investigated. The estimation error of training sample is weighted by corresponding density value and the potential contribution of training sample is obtained. Then the sample with the greatest value in the sorted spectrum of the potential contribution is selected as the support vector. The density and the potential contribution of training sample are updated and the potential contribution of the neighborhood sample of support vectors is significantly reduced. Thus the rechoosing of similar sample as support vector is properly avoided. More support vectors in the training sample set are iteratively selected, until the user-defined performance is achieved, thus the sparse LSSVM model is obtained. The simulation and practical applications indicate that the proposed method performs more effectively than Suykens standard sparse method for removing the redundant support vector with better sparseness and robustness.