We introduce the concept of span of support vectors (SV) and show that the generalization ability of support vector machines (SVM) depends on this new geometrical concept. We prove that the value of the span is always smaller (and can be much smaller) than the diameter of the smallest sphere containing the support vectors, used in previous bounds (Vapnik, 1998). We also demonstate experimentally that the prediction of the test error given by the span is very accurate and has direct application in model selection (choice of the optimal parameters of the SVM).

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