On the approximation capabilities of hard limiter feedforward neural networks

Authors:
Konstantinos Koutroumbas;Yannis Bakopoulos
Affiliations:
Institute for Space Applications and Remote Sensing, National Observatory of Athens, Greece;Computational Application Group, Division of Applied Technologies, NCSR Demokritos, Athens, Greece
Venue:
SETN'10 Proceedings of the 6th Hellenic conference on Artificial Intelligence: theories, models and applications
Year:
2010

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Abstract

In this paper the problem of the approximation of decision regions bordered by (a) closed and/or (b) open and unbounded convex hypersurfaces using feedforward neural networks (FNNs) with hard limiter nodes is considered Specifically, a constructive proof is given for the fact that a two or a three layer FNN with hard limiter nodes can approximate with arbitrary precision a given decision region of the above kind This is carried out in three steps First, each hypersurface is approximated by hyperplanes Then each one of the regions formed by the hypersurfaces is appropriately approximated by regions defined via the previous hyperplanes Finally, a feedforward neural network with hard limiter nodes is constructed, based on the previous hyperplanes and the regions defined by them.