Generalization properties of finite-size polynomial support vector machines

The learning properties of finite-size polynomial support vector machines are analyzed in the case of realizable classification tasks. The normalization of the high-order features acts as a squeezing factor, introducing a strong anisotropy in the patterns distribution in feature space. As a function...

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Bibliographic Details
Published in:Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000-11, Vol.62 (5 Pt B), p.7092-7099
Main Authors: Risau-Gusman, S, Gordon, MB
Format: Article
Language:English
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Summary:The learning properties of finite-size polynomial support vector machines are analyzed in the case of realizable classification tasks. The normalization of the high-order features acts as a squeezing factor, introducing a strong anisotropy in the patterns distribution in feature space. As a function of the training set size, the corresponding generalization error presents a crossover, more or less abrupt depending on the distribution's anisotropy and on the task to be learned, between a fast-decreasing and a slowly decreasing regime. This behavior corresponds to the stepwise decrease found by Dietrich et al. [Phys. Rev. Lett. 82, 2975 (1999)] in the thermodynamic limit. The theoretical results are in excellent agreement with the numerical simulations.
ISSN:1063-651X
1095-3787
DOI:10.1103/PhysRevE.62.7092