Skip to main content

A Non-Equidistant Elastic Net Algorithm

  • Chapter
Mathematics of Neural Networks

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 8))

  • 2313 Accesses

Abstract

The statistical mechanical derivation by Simic of the Elastic Net Algorithm (ENA) from a stochastic Hopfield neural network is criticized. In our view, the ENA should be considered a dynamic penalty method. Using a linear distance measure, a Non-equidistant Elastic Net Algorithm (NENA) is presented. Finally, a Hybrid Elastic Net Algorithm (HENA) is discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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. E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines, A Stochastic Approach to Combinatorial Optimization and Neural Computing, John Wiley & Sons (1989).

    Google Scholar 

  2. R. Durbin and D. Willshaw, An Analogue Approach of the Travelling Salesman Problem Using an Elastic Net Method, Nature, Vol. 326 (1987), pp689–691.

    Article  Google Scholar 

  3. J.H. Geselschap, Een Verbeterd ‘Elastic Net’ Algoritme (An Improved Elastic Net Algorithm), Master’s thesis, Erasmus University Rotterdam, Comp. Sc. Dept., (1994).

    Google Scholar 

  4. J. Hertz, A. Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley (1991).

    Google Scholar 

  5. J.J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proceedings of the National Academy of Sciences, USA Vol. 79 (1982), pp2554–2558.

    MathSciNet  Google Scholar 

  6. G. Parisi, Statistical Field Theory, Addison-Wesley (1988).

    Google Scholar 

  7. C. Peterson and B. Söderberg, Artificial Neural Networks and Combinatorial Optimization Problems, to appear in: Local Search in Combinatorial Optimization, E.H.L. Aarts and J.K. Lenstra eds., John Wiley & Sons.

    Google Scholar 

  8. P.D. Simic, Statistical Mechanics as the Underlying Theory of ‘Elastic’ and ‘Neural’ Optimisations, Network, Vol. 1 (1990), pp88–103.

    Article  MathSciNet  Google Scholar 

  9. J. van den Berg and J.C. Bioch, Constrained Optimization with the Hopfield-Lagrange Model, in: Proceedings of the 14th IMACS World Congress (1994), pp470–473.

    Google Scholar 

  10. J. van den Berg and J. C. Bioch, On the (Free) Energy of Stochastic and Continuous Hopfield Neural Networks, in: Neural Networks: The Statistical Mechanics Perspective, J.-H. Oh, C. Kwon, S. Cho eds., World Scientific (1995), pp233–244.

    Google Scholar 

  11. J. van den Berg and J.C. Bioch, Some Theorems Concerning the Free Energy of (Un)Constrained Stochastic Hopfield Neural Networks, in: Lecture Notes in Artificial Intelligence 904, EuroCOLT’95 (1995), pp298–312.

    Google Scholar 

  12. J. van den Berg and J.H. Geselschap, An analysis of various elastic net algorithms, Technical Report EUR-CS-95-06, Erasmus University Rotterdam, Comp. Sc. Dept. (1995).

    Google Scholar 

  13. A.L. Yuille, Generalized Deformable Models, Statistical Physics, and Matching Problems, Neural Computation, Vol. 2 (1990), pp1–24.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

van den Berg, J., Geselschap, J.H. (1997). A Non-Equidistant Elastic Net Algorithm. In: Ellacott, S.W., Mason, J.C., Anderson, I.J. (eds) Mathematics of Neural Networks. Operations Research/Computer Science Interfaces Series, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6099-9_14

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-6099-9_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7794-8

  • Online ISBN: 978-1-4615-6099-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics