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On the Partitioning Capabilities of Feedforward Neural Networks with Sigmoid Nodes

koutroum{at}space.noa.gr, Institute of Space Applications and Remote Sensing, National Observatory of Athens, 152 36 Athens, Greece

In this letter, the capabilities of feedforward neural networks (FNNs) on the realization and approximation of functions of the form g: ^l A, which partition the ^l 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.

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