PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Maximal margin classification for metric spaces
Matthias Hein, Olivier Bousquet and Bernhard Schölkopf
Journal of Computer and Systems Science 2004.


In order to apply the maximum margin method in arbitrary metric spaces, we suggest to embed the metric space into a Banach or Hilbert space and to perform linear classification in this space. We propose several embeddings and recall that an isometric embedding in a Banach space is always possible while an isometric embedding in a Hilbert space is only possible for certain metric spaces. As a result, we obtain a general maximum margin classification algorithm for arbitrary metric spaces (whose solution is approximated by an algorithm of Graepel et al. Interestingly enough, the embedding approach, when applied to a metric which can be embedded into a Hilbert space, yields the SVM algorithm, which emphasizes the fact that its solution depends on the metric and not on the kernel. Furthermore we give upper bounds of the capacity of the function classes corresponding to both embeddings in terms of Rademacher averages. Finally we compare the capacities of these function classes directly.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:587
Deposited By:Matthias Hein
Deposited On:26 December 2004