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A Guide for the Upper Bound on the Number of Continuous-Valued Hidden Nodes of a Feed-Forward Network

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Artificial Neural Networks – ICANN 2009 (ICANN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5768))

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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.

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References

  1. Arai, M.: Bounds on the number of hidden units in binary-valued three-layer neural networks. Neural Networks 6, 855–860 (1993)

    Article  Google Scholar 

  2. Arslanov, M.Z., Ashigaliev, D.U., Ismail, E.E.: N-bit parity ordered neural networks. Neurocomputing 48, 1053–1056 (2002)

    Article  MATH  Google Scholar 

  3. Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Addison-Wesley Publishing Company, Redwood City (1991)

    Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Lavretsky, E.: On the exact solution of the Parity-N problem using ordered neural networks. Neural Networks 13(8), 643–649 (2000)

    Article  Google Scholar 

  9. 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)

    Article  MATH  Google Scholar 

  10. Munkres, J.: Topology: a first course. Prentice-Hall, Englewood Cliffs (1975)

    MATH  Google Scholar 

  11. Murty, K.: Linear Programming. John Wiley & Sons, NY (1983)

    MATH  Google Scholar 

  12. Setiono, R.: On the solution of the parity problem by a single hidden layer feedforward neural network. Neurocomputing 16, 225–235 (1997)

    Article  MATH  Google Scholar 

  13. Sontag, E.: Feedforward nets for interpolation and classification. J. Comput. System Sci. 45, 20–48 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tsaih, R.: An explanation of reasoning neural networks. Mathematical and Computer Modelling 28, 37–44 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Management Information Systems, National Chengchi University, Taipei, 116, Taiwan

    Rua-Huan Tsaih

  2. Graduate Institute of Global Operations Strategy and Logistics Management, National Dong Hwa University, 974, Taiwan

    Yat-wah Wan

Authors
  1. Rua-Huan Tsaih
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  2. Yat-wah Wan
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy

    Cesare Alippi

  2. Department of Electrical and Computer Engineering, University of Cyprus, 75 Kallipoleos Street, 1678, Nicosia, Cyprus

    Marios Polycarpou , Christos Panayiotou  & Georgios Ellinas ,  & 

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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

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  • 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)

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