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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 applicationdoi:10.1162/089976600300015042 pmid:10976137 fatcat:k5yuyngpznamrfemyuzaq5a34m