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We show that the recently proposed variant of the Support Vector machine (SVM) algorithm, known as v-SVM, can be interpreted as a maximal separation between subsets of the convex hulls of the data, which we call soft convex hulls. The soft convex hulls are controlled by choice of the parameter v. If the intersection of the convex hulls is empty, the… (More)

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 solutions. We note that… (More)

Kernel methods have attracted wide interest in the machine learning community over the last few years. Their appeal lies in their performance as algorithms and in their rich mathematical context and tractability. In this work 1 , we address the question of when a kernel algorithm has a unique solution, using support vector machines for classification and… (More)

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