05305387

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05305387 Carrizosa, Emilio Support vector machines and distance minimization. Pardalos, Panos M. (ed.) et al., Data mining and mathematical programming. Chapters of the book are based on lectures at the workshop, Montreal, Canada, October 10--13, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4352-9/pbk). CRM Proceedings and Lecture Notes 45, 1-13 (2008). 2008 Providence, RI: American Mathematical Society (AMS) EN Summary: Support vector machine is a powerful classification tool of increasing popularity in data mining. When, as customary in practice, the sets to be classified are not separable, the so-called soft-margin approach is often used as a surrogate of the maximization of the margin. In this note we show that different soft-margin problems already studied in the literature, as well as some of their extensions, can be formulated as minimum-distance problems. Using the machinery of convex analysis, optimality conditions are derived for such minimum-distance problems, yielding, in particular, a characterization for degeneracy.