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Eigenvalue Problem Approach to Discrete Minimization

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Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005 (ICANN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3697))

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Abstract

The problem of finding of the deepest local minimum of a quadratic functional of binary variables is discussed. Our approach is based on the asynchronous neural dynamics and utilizes the eigenvalues and eigenvectors of the connection matrix. We discuss the role of the largest eigenvalues. We report the results of intensive computer experiments with random matrices of large dimensions N ~ 102–103.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/11550907_163 .

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References

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

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Author information

Authors and Affiliations

  1. Institute of Optical Neural Technologies, Russian Academy of Sciences, Moscow, Russia

    Leonid B. Litinskii

Authors
  1. Leonid B. Litinskii
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Editor information

Editors and Affiliations

  1. Department of Informatics, Nicolaus Copernicus University, Toruń, Poland

    Włodzisław Duch

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

  3. Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, 02015, HUT, Finland

    Erkki Oja

  4. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Sławomir Zadrożny

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© 2005 Springer-Verlag Berlin Heidelberg

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Litinskii, L.B. (2005). Eigenvalue Problem Approach to Discrete Minimization. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550907_64

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  • DOI: https://doi.org/10.1007/11550907_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28755-1

  • Online ISBN: 978-3-540-28756-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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