摘要： 高斯核函数因其良好的性态，在新近提出的学习机器——支撑向量机中得到广泛的应用，以高斯核为其核函数的支撑向量机在实际应用中表现出良好的学习性能。然而，研究发现，高斯核中尺度参数σ的大小对支撑向量机性能的优劣发挥着关键性的作用。该文研究和讨论了支撑向量机的性能随尺度参数σ从0到∞的变化规律，证明了高斯核支撑向量机在σ→0和σ→∞时所具有的重要性质。数值实验结果进一步验证了所得结论。

关键词: 支撑向量机, 高斯核, 尺度参数

Abstract: Gauss kernel function is widely used in support vector machines (SVM) because of its good properties. However, many applications demonstrate that the performance of SVM with Gauss kernel is influenced greatly by the scale parameterσ.In this paper,the authors show how the parameterσ affects the function of SVM with Gauss kernel. It is also proved that whenσ→0 , all the training samples are classified correctly by SVM with Gauss kernel, but the SVM can only get a constant function whenσ→∞. In both cases, SVM with Gauss kernel has little generalization ability. Experimental results validate the conclusion.

中图分类号: 

• TP181