基于几何分析的支持向量机推广能力推测模型

SVM Generalization Performance Measuring Model Based on Geometry Analysis

利用支持向量机分类器中支持向量分布的几何意义,构造了一种新的与样本分布相关的推广能力预测模型,该模型充分利用了支持向量分布的先验信息,它与统计学习理论中推广能力准则具有一致的几何意义。首先利用支持向量分布的几何意义出发从海量样本中选择有效边界向量代替原有训练样本,然后在有效边界向量中分别计算最小包含半径和最大分类间隔。它不需要求解二次规划就可以得到与训练样本相关的推广能力计算模型,计算量较低。本文最后的最优核函数、核参数选择仿真实验结果表明本文提出的基于几何分析的支持向量机推广能力推测模型的合理性与高效性,该模型对于解决支持向量机中最优核函数、核参数选择具有重要意义。

A new support vector machine generalization performance measuring model which bases on the geometry principle of support vectors and its distribution is proposed in this paper. The principle is consistent in geometry with that in statistical learning theory and it makes good use of the support vector distribution prior information. Firstly some margin vectors are chose by nearest interclass dis- tance analysis, and then the minimum radius and maximum margin are computed to establish generalization performance measuring mod- els. It is important that this new principle can be processed before solving support vector machine quadratic programming difficult prob- lem and the load of computing is lower. The simulation results demonstrate that the proposed model in this paper is valid and effective and it is significant in searching optimal kernel function and kernel parameters to improve support vector machine performance.