Asymptotic Behaviour of Support Vector Machines
نویسنده
چکیده
A better submitted version of this paper is available at http://eric.univ-lyon2.fr/~ oteytaud. This report only completes the paper for some results of lower interest and we suggest that interested readers rst read the submitted version and only completes this reading by this paper if they want more information on some results not detailed in the submitted version. This report was rst written in June 1999 and revised in May 2000. We study the asymptotic behaviour of support vector machines, exhibiting especially some cases of bad behaviour: cases in which the error rate is higher than what might allow one-hidden-layer networks, even if the number of examples increases towards +1, and cases in which the number of support vectors increases towards +1. In order to prove these results, we use continuous problems as approximations of discrete ones. Di erent cases are distinguished: constant or variable penalization of errors; linear, polynomial or RBF kernel. We evoke concrete applications of these results to the approximation of minimas on big subsets by the mean of minimas on smaller subsets.
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تاریخ انتشار 2000