Generalization properties of finite size polynomial Support Vector Machines

Abstract

12 pages, 7 figuresThe 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 behaviour corresponds to the stepwise decrease found by Dietrich et al.[Phys. Rev. Lett. 82 (1999) 2975-2978] in the thermodynamic limit. The theoretical results are in excellent agreement with the numerical simulations