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Maximal Margin Classification for Metric Spaces

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons83958

Hein,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83824

Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Hein, M., & Bousquet, O. (2004). Maximal Margin Classification for Metric Spaces. In 16. Annual Conference on Computational Learning Theory / COLT Kernel 2003 (pp. 72-86). Heidelberg, Germany: Springer Verlag.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-D9D5-B
Zusammenfassung
In this article we construct a maximal margin classification algorithm for arbitrary metric spaces. At first we show that the Support Vector Machine (SVM) is a maximal margin algorithm for the class of metric spaces where the negative squared distance is conditionally positive definite (CPD). This means that the metric space can be isometrically embedded into a Hilbert space, where one performs linear maximal margin separation. We will show that the solution only depends on the metric, but not on the kernel. Following the framework we develop for the SVM, we construct an algorithm for maximal margin classification in arbitrary metric spaces. The main difference compared with SVM is that we no longer embed isometrically into a Hilbert space, but a Banach space. We further give an estimate of the capacity of the function class involved in this algorithm via Rademacher averages. We recover an algorithm of Graepel et al. [6].