On the Capabilities of Higher-Order Neurons: A Radial Basis Function Approach

Authors:
Michael Schmitt
Affiliations:
Lehrstuhl Mathematik und Informatik, Fakultät für Mathematik, Ruhr-Universität Bochum, D–44780 Bochum, Germany
Venue:
Neural Computation
Year:
2005

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Abstract

Higher-order neurons with k monomials in n variables are shown to have Vapnik-Chervonenkis (VC) dimension at least nk + 1. This result supersedes the previously known lower bound obtained via k-term monotone disjunctive normal form (DNF) formulas. Moreover, it implies that the VC dimension of higher-order neurons with k monomials is strictly larger than the VC dimension of k-term monotone DNF. The result is achieved by introducing an exponential approach that employs gaussian radial basis function neural networks for obtaining classifications of points in terms of higher-order neurons.