Skip to main content
SpringerLink
Log in

Yes,Trees May Have Neurons

60 Varieties of Trees

  • Chapter
  • First Online:
Computer Science in Perspective

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2598))

  • 654 Accesses

Abstract

Neural Trees are introduced. These descendants of decision trees are used to represent (approximations to) arbitrary continuous functions. They support efficient evaluation and the application of arithmetic operations, differentiation and definite integration.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Thomas Ottmann. Bäume in der informatik. Technical Report 13, Institut für Informatik, Universität Freiburg, June 1988.

    Google Scholar 

  2. Thomas Ottmann. Trees-a personal view. In Hermann A. Maurer, editor, New Results and New Trends in Computer Science, volume 555 of Lecture Notes in Computer Science, pages 243–255. Springer, 1991.

    Chapter  Google Scholar 

  3. Alois P. Heinz. A tree-structured neural network for real-time adaptive control. In S. Amari, L. Xu, L.-W. Chan, I. King, and K.-S. Leung, editors, Progress in Neural Information Pro-cessing, Proceedings of the International Conference on Neural Information Processing, Hong Kong, volume 2, pages 926–931, Berlin, September 1996. Springer.

    Google Scholar 

  4. J. C. Burkill and H. Burkill. A Second Course in Mathematical Analysis. Cambridge University Press, Cambridge, England, 1970.

    MATH  Google Scholar 

  5. Alois P. Heinz. On a class of constructible neural networks. In Françoise Fogelman-Soulié and Patrick Gallinari, editors, ICANN’ 95, Proceedings of the International Conference on Artificial Neural Networks, Paris, France, volume 1, pages 563–568, Paris La Défense, France, October 1995. EC2 & Cie.

    Google Scholar 

  6. J. Kindermann and A. Linden. Inversion of neural networks by gradient descent. Journal of Parallel Computing, 14(3):277–286, 1992.

    Article  Google Scholar 

  7. D. DeMers and K. Kreutz-Delgado. Solving inverse kinematics for redundant manipulators. In O. Omidvar and P. van Smagt, editors, Neural Systems for Robotics, pages 75–112. Academic Press, New York, 1997.

    Google Scholar 

  8. M. Brown and C. Harris. Neurofuzzy Adaptive Modelling and Control. Systems and Control Engineering. Prentice Hall International, London, UK, 1994.

    Google Scholar 

  9. J. E. Dennis and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ, 1983.

    MATH  Google Scholar 

  10. R. E. Wengert. A simple automatic derivative evaluation program. Comm. ACM, 7(8):463–464, 1964.

    Article  MATH  Google Scholar 

  11. A. E. Bryson and Y.-C. Ho. Applied Optimal Control. Blaisdell, New York, 1969. [Revised printing New York: Hemisphere, 1975].

    Google Scholar 

  12. W. Baur and V. Strassen. The complexity of partial derivatives. Theoretical Computer Science, 22:317–330, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. E. Rumelhart, G. E. Hinton, and R. J. Williams. Learning representations by back-propagating errors. Nature, 323:533–536, 1986.

    Article  Google Scholar 

  14. T. Yoshida. Derivation of a computational process for partial derivatives of functions using transformations of a graph. Transactions of Information Processing Society of Japan, 11(19):1112–1120, 1987.

    Google Scholar 

  15. A. Griewank and S. Reese. On the calculation of Jacobian matrices by the Markowitz rule. In [17], pages 126–135. SIAM, 1991.

    MathSciNet  Google Scholar 

  16. T. Yoshida. A node elimination rule for the calculation of Jacobian matrices. In Proceedings of the Second International SIAM Workshop on Computational Differentiation, Santa Fe, NM, Philadelphia, 1996. SIAM.

    Google Scholar 

  17. A. Griewank and G. F. Corliss, editors. Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM, Philadelphia, Penn., 1991.

    MATH  Google Scholar 

  18. Alois P. Heinz. Efficient top-down jacobian evaluation of tree-structured neural networks. In Lars Niklasson, Mikael Bodén, and Tom Ziemke, editors, ICANN 98, Proceedings of the 8th International Conference on Artificial Neural Networks, Skövde, Sweden, volume I, pages 87–92. Springer-Verlag, 1998.

    Google Scholar 

  19. Graeme Fairweather and Rick D. Saylor. The reformulation and numerical solution of certain nonclassical initial-boundary value problems. SIAM Journal on Scientific and Statistical Computing, 12(1):127–144, January 1991.

    Article  MATH  MathSciNet  Google Scholar 

  20. A. C. Norman and J. H. Davenport. Symbolic integration-the dust settles? In Proc. EU-ROSAM 1979, Lecture Notes in Computer Science, volume 72, pages 398–407. Springer-Verlag, 1979.

    Google Scholar 

  21. R. Cranley and T. N. L. Patterson. On the automatic numerical evaluation of definite integrals. The Computer Journal, 14(2):189–198, May 1971.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Applied Sciences Heilbronn, Max-Planck-Str. 39, D-74081, Heilbronn

    Alois P. Heinz

Authors
  1. Alois P. Heinz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Universität Bonn, Informatik I, Römerstraße 164, 53117, Bonn, Germany

    Rolf Klein

  2. Praktische Informatik III, FernUniversität Hagen, Informatikzentrum Universitätsstraße 1, 58084, Hagen, Germany

    Hans-Werner Six

  3. Praktische Informatik - Datenbanken, Universität Kassel, 34109, Kassel, Germany

    Lutz Wegner

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Heinz, A.P. (2003). Yes,Trees May Have Neurons. In: Klein, R., Six, HW., Wegner, L. (eds) Computer Science in Perspective. Lecture Notes in Computer Science, vol 2598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36477-3_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-36477-3_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00579-7

  • Online ISBN: 978-3-540-36477-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation