Uniqueness of the SVM Solution

Part of Advances in Neural Information Processing Systems 12 (NIPS 1999)

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Christopher J. C. Burges, David Crisp


We give necessary and sufficient conditions for uniqueness of the support vector solution for the problems of pattern recognition and regression estimation, for a general class of cost functions. We show that if the solution is not unique, all support vectors are necessarily at bound, and we give some simple examples of non-unique solu(cid:173) tions. We note that uniqueness of the primal (dual) solution does not necessarily imply uniqueness of the dual (primal) solution. We show how to compute the threshold b when the solution is unique, but when all support vectors are at bound, in which case the usual method for determining b does not work.