Geometrical Properties of Nu Support Vector Machines with Different Norms
Geometrical Properties of Nu Support Vector Machines with Different Norms
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DOI：
10.1162/0899766054796897
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发表时间：
2005-11
影响因子：
2.9
通讯作者：
K. Ikeda;Noboru Murata
中科院分区：
文献类型：
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作者：
K. Ikeda;Noboru Murata
通过采用 L1 或 L 范数来最大化边际，支持向量机 (SVM) 会产生线性规划问题，与具有 L2 范数的 SVM 相比，该问题需要更低的计算负载。然而，除了数值实验之外，范数的变化如何影响SVM的泛化能力到目前为止还没有得到阐明。在这封信中，研究了具有 Lp 范数的 SVM 的几何意义，并且表明 SVM 解对 p 的依赖性相当小。
By employing the L1 or L norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L2 norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the Lp norm is investigated, and the SVM solutions are shown to have rather little dependency on p.