On the partitioning capabilities of feedforward neural networks with sigmoid nodes

Authors:
K. Koutroumbas
Affiliations:
Institute of Space Applications and Remote Sensing, National Observatory of Athens, 152 36 Athens, Greece
Venue:
Neural Computation
Year:
2003

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Abstract

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