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.
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References
Barron, A.: Universal approximation bounds for superposition of a sigmoidal function. IEEE Transactions on Information Theory 3, 930–945 (1993)
Blum, E., Li, K.: Approximation theory and feedforward networks. Neural Networks 4, 511–515 (1991)
Cybenko, G.: Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems 2, 304–314 (1989)
Geva, S., Sitte, J.: A constructive method for multivariate function approximation by multilayer perceptrons. IEEE Transactions on Neural Networks 3(4), 621–623 (1992)
Gibson, G.J., Cowan, C.F.N.: On the decision regions of multilayer perceptrons. Proceedings of the IEEE 78(10), 1590–1594 (1990)
Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989)
Lelek, A.: Introduction to set theory and topology. Trohalia (translated in Greek) (1992)
Lippmann, R.P.: An introduction to computing with neural networks. IEEE ASSP Magazine 4(2), 4–22 (1987)
Sandberg, I.W.: General structures for classification. IEEE Transactions on Circuits and Systems I 41(5), 372–376 (1994)
Sarselli, F., Tsoi, A.C.: Universal approximation using feedforward neural networks: A survey of some existing methods and some new results. Neural Networks 11(1), 15–37 (1998)
Selmic, R.R., Lewis, F.L.: Neural network approximation of piecewise continuous functions: application to friction compensation. IEEE Transactions on Neural Networks 13(3), 745–751 (2002)
Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn. Academic Press, London (2009)
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Koutroumbas, K., Bakopoulos, Y. (2010). On the Approximation Capabilities of Hard Limiter Feedforward Neural Networks. In: Konstantopoulos, S., Perantonis, S., Karkaletsis, V., Spyropoulos, C.D., Vouros, G. (eds) Artificial Intelligence: Theories, Models and Applications. SETN 2010. Lecture Notes in Computer Science(), vol 6040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12842-4_20
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DOI: https://doi.org/10.1007/978-3-642-12842-4_20
Publisher Name: Springer, Berlin, Heidelberg
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