Sparseness of Support Vector Machines---Some Asymptotically Sharp Bounds

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Ingo Steinwart


The decision functions constructed by support vector machines (SVM’s) usually depend only on a subset of the training set—the so-called support vectors. We derive asymptotically sharp lower and upper bounds on the number of support vectors for several standard types of SVM’s. In par- ticular, we show for the Gaussian RBF kernel that the fraction of support vectors tends to twice the Bayes risk for the L1-SVM, to the probability of noise for the L2-SVM, and to 1 for the LS-SVM.