From Continuous Behaviour to Discrete Knowledge

  • Agapito Ledezma
  • Fernando Fernández
  • Ricardo Aler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2687)


Neural networks have proven to be very powerful techniques for solving a wide range of tasks. However, the learned concepts are unreadable for humans. Some works try to obtain symbolic models from the networks, once these networks have been trained, allowing to understand the model by means of decision trees or rules that are closer to human understanding. The main problem of this approach is that neural networks output a continuous range of values, so even though a symbolic technique could be used to work with continuous classes, this output would still be hard to understand for humans. In this work, we present a system that is able to model a neural network behaviour by discretizing its outputs with a vector quantization approach, allowing to apply the symbolic method.


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  1. 1.
    D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986.CrossRefGoogle Scholar
  2. 2.
    Leslie P. Kaelbling, Michael L. Littman, and Andrew W. Moore, “Reinforcement learning: A survey,” Int. J. of Artificial Intelligence Research, pp. 237–285, 1996.Google Scholar
  3. 3.
    Antonio Berlanga, Araceli Sanchis, Pedro Isasi, and José M. Molina, “A general coevolution method to generalize autonomous robot navigation behavior,” in Proceedings of the Congress on Evolutionary Computation, La Jolla, San Diego (CA) USA, July 2000, pp. 769–776, IEEE Press.Google Scholar
  4. 4.
    Jude W. Shavlik and Geoffrey G. Towell, Machine Learning. A Multistrategy Approach., vol. IV, chapter Refining Symbolic Knowledge using Neural Networks, pp. 405–429, Morgan Kaufmann, 1994.Google Scholar
  5. 5.
    Ricardo Aler, Daniel Borrajo, Inés Galván,, and Agapito Ledezma, “Learning models of other agents,” in Proceedings of the Agents-00/ECML-00 Workshop on Learning Agents,, Barcelona, Spain, June 2000, pp. 1–5.Google Scholar
  6. 6.
    J. R. Quinlan, “Induction of decision trees,” Machine Learning, vol. 1, no. 1, pp. 81–106, 1986.Google Scholar
  7. 7.
    S. P. Lloyd, “Least squares quantization in pcm,” Unpublished Bell Laboratories Technical Note. Portions presented at the Institute of Mathematical Statistics Meeting Atlantic City, New Jersey, September 1957. Published in the March 1982 special issue on quantization of the IEEE Transactions on Information Theory, 1957.Google Scholar
  8. 8.
    J. Ross Quinlan, C4.5: Programs for Machine Learning, Morgan Kaufmann, San Mateo, CA, 1993.Google Scholar
  9. 9.
    L. Breiman, J.H. Friedman, K.A. Olshen, and C.J. Stone, Classification and Regression Tress, Wadsworth & Brooks, Monterey, CA (USA), 1984.MATHGoogle Scholar
  10. 10.
    J. Ross Quinlan, “Combining instance-based and model-based learning,” in Proceedings of the Tenth International Conference on Machine Learning, Amherst, MA, June 1993, pp. 236–243, Morgan Kaufmann.Google Scholar
  11. 11.
    Antonio Berlanga Agapito Ledezma and Ricardo Aler, “Extracting knowledge from reactive robot behaviour,” in Proceedings of the Agents-01/Workshop on Learning Agents,, Montreal, Canada, 2001, pp. 7–12.Google Scholar
  12. 12.
    Allen Gersho and Robert M. Gray, Vector Quantization and Signal Compression, Kluwer Academic Publishers, 1992.Google Scholar
  13. 13.
    Fernando Fernández and Daniel Borrajo, “VQQL. Applying vector quantization to reinforcement learning,” in RoboCup-99: Robot Soccer World Cup III, number 1856 in Lecture Notes in Artificial Intelligence, pp. 292–303. Springer Verlag, 2000.Google Scholar
  14. 14.
    V. Braitenberg, Vehicles: experiments on synthetic psychology, MIT Press, Massachusets, 1984.Google Scholar
  15. 15.
    J. Ross Quinlan, C4.5: Programs for Machine Learning, Morgan Kaufmann, 1993.Google Scholar
  16. 16.
    L. Sommaruga, I. Merino, V. Matellán, and J.M. Molina, “A distributed simulator for intelligent autonomous robots,” in In Proccedings of Fourth International Symposium on Intelligent Robotic Systems, 1996, pp. 393–399.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Agapito Ledezma
    • 1
  • Fernando Fernández
    • 1
  • Ricardo Aler
    • 1
  1. 1.Universidad Carlos III de MadridLeganés, MadridSpain

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