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Geometrical properties of Nu support vector machines with different norms. (English) Zbl 1075.68074

Summary: By employing the \(L_1\) or \(L_{\infty}\) 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 \(L_2\) 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 \(L_p\) norm is investigated, and the SVM solutions are shown to have rather little dependency on \(p\).

MSC:

68T05 Learning and adaptive systems in artificial intelligence
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