Skip to main content

Cluster Domains in Binary Minimization Problems

  • Conference paper
Artificial Neural Networks – ICANN 2007 (ICANN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4668))

Included in the following conference series:

  • 2651 Accesses

Abstract

Previously it was found that when minimizing a quadratic functional depending on a great number of binary variables, it is reasonable to use aggregated variables, joining together independent binary variables in blocks (domains). Then one succeeds in finding deeper local minima of the functional. In the present publication we investigate an algorithm of the domains formation based on the clustering of the connection matrix.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Hartmann, A.K., Rieger, H.: Optimization Algorithms in Physics. Wiley-VCH, Berlin (2001)

    Google Scholar 

  2. Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Addison-Wesley, Reading (1991)

    Google Scholar 

  3. Kryzhanovskii, B.V., Magomedov, B.M., Mikaelyan, A.L.: A Domain Model of a Neural Network. Doklady Mathematics 71(2), 310–314 (2005)

    Google Scholar 

  4. Kryzhanovsky, B., Magomedov, B.: On the Probability of Finding Local Minima in Optimization Problems. In: Proceedings of IJCNN’2006, Vancouver, pp. 5882–5887 (2006)

    Google Scholar 

  5. Herz, A.V.M., Marcus, C.M.: Distributed dynamics in neural networks. Physical Review E47, 2155–2161 (1993)

    Google Scholar 

  6. Litinskii, L.B.: Direct calculation of the stable points of a neural network. Theoretical and Mathematical Physics 101(3), 1492–1501 (1994)

    Article  Google Scholar 

  7. Xu, R., Wunsh II, D.: Survey of Clustering Algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)

    Article  Google Scholar 

  8. Li, T., Zhu, S., Ogihara, M.: Algorithms for clustering high dimensional and distributed data. Intelligent Data Analysis 7, 305–326 (2003)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Joaquim Marques de Sá Luís A. Alexandre Włodzisław Duch Danilo Mandic

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Litinskii, L.B. (2007). Cluster Domains in Binary Minimization Problems. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74690-4_65

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74690-4_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74689-8

  • Online ISBN: 978-3-540-74690-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics