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0899-7667
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1530-888X
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Neural Computation

October 1, 2003, Vol. 15, No. 10, Pages 2457-2481
(doi: 10.1162/089976603322362437)
© 2003 Massachusetts Institute of Technology
On the Partitioning Capabilities of Feedforward Neural Networks with Sigmoid Nodes
Article PDF (254.33 KB)
Abstract

In this letter, the capabilities of feedforward neural networks (FNNs) on the realization and approximation of functions of the form g: R1A, which partition the R1 space into polyhedral sets, each one being assigned to one out of the c classes of A, are investigated. More specifically, a constructive proof is given for the fact that FNNs consisting of nodes having sigmoid output functions are capable of approximating any function g with arbitrary accuracy. Also, the capabilities of FNNs consisting of nodes having the hard limiter as output function are reviewed. In both cases, the two-class as well as the multiclass cases are considered.