Abstract
This study proposes and validates a construction concept for the realization of a real-valued single-hidden layer feed-forward neural network (SLFN) with continuous-valued hidden nodes for arbitrary mapping problems. The proposed construction concept says that for a specific application problem, the upper bound on the number of used hidden nodes depends on the characteristic of adopted SLFN and the observed properties of collected data samples. A positive validation result is obtained from the experiment of applying the construction concept to the m-bit parity problem learned by constructing two types of SLFN network solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arai, M.: Bounds on the number of hidden units in binary-valued three-layer neural networks. Neural Networks 6, 855–860 (1993)
Arslanov, M.Z., Ashigaliev, D.U., Ismail, E.E.: N-bit parity ordered neural networks. Neurocomputing 48, 1053–1056 (2002)
Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Addison-Wesley Publishing Company, Redwood City (1991)
Hohil, M.E., Liu, D.R., Smith, S.H.: Solving the N-bit parity problem using neural networks. Neural Networks 12(11), 1321–1323 (1999)
Huang, G., Babri, H.: Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions. IEEE Transactions on Neural Networks 9, 224–229 (1998)
Huang, S.C., Huang, Y.F.: Bounds on the number of hidden neurons in multilayer perceptrons. IEEE Transactions on Neural Networks 2, 47–55 (1991)
Iyoda, E.M., Nobuhara, H., Hirota, K.: A solution for the N-bit parity problem using a single translated multiplicative neuron. Neural Processing Letters 18(3), 213–218 (2003)
Lavretsky, E.: On the exact solution of the Parity-N problem using ordered neural networks. Neural Networks 13(8), 643–649 (2000)
Liu, D.R., Hohil, M.E., Smith, S.H.: N-bit parity neural networks: new solutions based on linear programming. Neurocomputing 48, 477–488 (2002)
Munkres, J.: Topology: a first course. Prentice-Hall, Englewood Cliffs (1975)
Murty, K.: Linear Programming. John Wiley & Sons, NY (1983)
Setiono, R.: On the solution of the parity problem by a single hidden layer feedforward neural network. Neurocomputing 16, 225–235 (1997)
Sontag, E.: Feedforward nets for interpolation and classification. J. Comput. System Sci. 45, 20–48 (1992)
Tsaih, R.: An explanation of reasoning neural networks. Mathematical and Computer Modelling 28, 37–44 (1998)
Urcid, G., Ritter, G.X., Iancu, L.: Single layer morphological Perceptron solution to the N-bit parity problem. In: Sanfeliu, A., Martínez Trinidad, J.F., Carrasco Ochoa, J.A. (eds.) CIARP 2004. LNCS, vol. 3287, pp. 171–178. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tsaih, RH., Wan, Yw. (2009). A Guide for the Upper Bound on the Number of Continuous-Valued Hidden Nodes of a Feed-Forward Network. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds) Artificial Neural Networks – ICANN 2009. ICANN 2009. Lecture Notes in Computer Science, vol 5768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04274-4_68
Download citation
DOI: https://doi.org/10.1007/978-3-642-04274-4_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04273-7
Online ISBN: 978-3-642-04274-4
eBook Packages: Computer ScienceComputer Science (R0)