On the capabilities of higher-order neurons: a radial basis function approach.
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.
Schmitt
Michael
M
Lehrstuhl Mathematik und Informatik, Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany. mschmitt@lmi.ruhr-uni-bochum.de
D000465:Algorithms; D000818:Animals; D001185:Artificial Intelligence; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*