An asymptotic statistical analysis of support vector machines with soft margins
An asymptotic statistical analysis of support vector machines with soft margins
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DOI：
10.1016/j.neunet.2004.11.008
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发表时间：
2005-04
期刊：
影响因子：
7.8
通讯作者：
K. Ikeda;Tsutomu Aoishi
中科院分区：
文献类型：
--
作者：
K. Ikeda;Tsutomu Aoishi
研究了支持向量机的泛化特性。从几何的角度来看，SVM的估计参数是由给定的例子形成的凸船体中最接近原点的一个。由于引入软边界相当于减少了样本的凸船体，因此具有软边界的SVM具有与原始SVM不同的学习曲线。本文在简单的情况下，即仅当输入维数为1时，导出了具有软边界的支持向量机的渐近平均推广误差，并定量地证明了软边界会增加推广误差。
The generalization properties of support vector machines (SVMs) are examined. From a geometrical point of view, the estimated parameter of an SVM is the one nearest the origin in the convex hull formed with given examples. Since introducing soft margins is equivalent to reducing the convex hull of the examples, an SVM with soft margins has a different learning curve from the original. In this paper we derive the asymptotic average generalization error of SVMs with soft margins in simple cases, that is, only when the dimension of inputs is one, and quantitatively show that soft margins increase the generalization error.