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On Constructing Threshold Networks for Pattern Classification

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 258))

Abstract

This paper describes a method of constructing one-hidden layer feedforward linear threshold networks to represent Boolean functions (or partially-defined Boolean functions). The first step in the construction is sequential linear separation, a technique that has been used by a number of researchers [7, 11, 2]. Next, from a suitable sequence of linear separations, a threshold network is formed. The method described here results in a threshold network with one hidden layer. We compare this approach to the standard approach based on a Boolean function’s disjunctive normal form and to other approaches based on sequential linear separation [7, 11].

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References

  1. Anthony, M.: Discrete Mathematics of Neural Networks: Selected Topics. Society for Industrial and Applied Mathematics, Philadeplhia (2001)

    MATH  Google Scholar 

  2. Anthony, M.: On data classification by iterative linear partitioning. Discrete Applied Mathematics 144(1-2), 2–16 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cover, T.M.: Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition. IEEE Trans. on Electronic Computers EC-14, 326–334 (1965)

    Article  Google Scholar 

  4. Hammer, P.L., Ibaraki, T., Peled., U.N.: Threshold numbers and threshold completions. Annals of Discrete Mathematics 11, 125–145 (1981)

    MATH  MathSciNet  Google Scholar 

  5. Jeroslow, R.G.: On defining sets of vertices of the hypercube by linear inequalities. Discrete Mathematics 11, 119–124 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  6. Krause, M.: On the computational power of boolean decision lists. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 372–383. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  7. Marchand, M., Golea, M.: On Learning Simple Neural Concepts: from Halfspace Intersections to Neural Decision Lists. Network: Computation in Neural Systems 4, 67–85 (1993)

    Article  Google Scholar 

  8. Marchand, M., Golea, M., Ruján, P.: A convergence theorem for sequential learning in two-layer perceptrons. Europhys. Lett. 11, 487 (1990)

    Article  Google Scholar 

  9. Rivest, R.R.: Learning Decision Lists. Machine Learning 2(3), 229–246 (1987)

    Google Scholar 

  10. Siu, K.Y., Rowchowdhury, V., Kalaith, T.: Discrete Neural Computation: A Theoretical Foundation. Prentice Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  11. Tajine, M., Elizondo, D.: Growing methods for constructing Recursive Deterministic Perceptron neural networks and knowledge extraction. Artificial Intelligence 102, 295–322 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Tajine, M., Elizondo, D.: The recursive deterministic perceptron neural network. Neural Networks 11, 1571–1588 (1998)

    Article  Google Scholar 

  13. Turán, G., Vatan, F.: Linear decision lists and partitioning algorithms for the construction of neural networks. In: Foundations of Computational Mathematics: selected papers of a conference, Rio de Janeiro, pp. 414–423. Springer, Heidelberg (1997)

    Google Scholar 

  14. Zuev, A., Lipkin, L.I.: Estimating the efficiency of threshold representations of Boolean functions. Cybernetics 24, 713–723 (1988); Translated from Kibernetika (Kiev) 6, 29–37 (1988)

    Article  MATH  MathSciNet  Google Scholar 

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Anthony, M. (2009). On Constructing Threshold Networks for Pattern Classification. In: Franco, L., Elizondo, D.A., Jerez, J.M. (eds) Constructive Neural Networks. Studies in Computational Intelligence, vol 258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04512-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-04512-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04511-0

  • Online ISBN: 978-3-642-04512-7

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