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ISSN
0899-7667
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1530-888X
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Neural Computation

March 1, 2005, Vol. 17, No. 3, Pages 715-729
(doi: 10.1162/0899766053019953)
© 2005 Massachusetts Institute of Technology
On the Capabilities of Higher-Order Neurons: A Radial Basis Function Approach
Article PDF (108.27 KB)
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 viak-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.