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 contain
ing the support vectors, used in previous bounds (Vapnik, 1998). We also de
monstate 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).