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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
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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.