Journal
JOURNAL OF COMPUTER AND SYSTEM SCIENCES
Volume 71, Issue 3, Pages 333-359Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcss.2004.10.013
Keywords
classification; maximum margin; metric spaces; embedding; pattern recognition
Ask authors/readers for more resources
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. (International Conference on Artificial Neural Networks 1999, pp. 304-309)). Interestingly enough, the embedding approach, when applied to a metric which can be embedded into a Hilbert space, yields the support vector machine (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. (c) 2004 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available