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.
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References
Hartmann, A.K., Rieger, H.: Optimization Algorithms in Physics. Wiley-VCH, Berlin (2001)
Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Addison-Wesley, Reading (1991)
Kryzhanovskii, B.V., Magomedov, B.M., Mikaelyan, A.L.: A Domain Model of a Neural Network. Doklady Mathematics 71(2), 310–314 (2005)
Kryzhanovsky, B., Magomedov, B.: On the Probability of Finding Local Minima in Optimization Problems. In: Proceedings of IJCNN’2006, Vancouver, pp. 5882–5887 (2006)
Herz, A.V.M., Marcus, C.M.: Distributed dynamics in neural networks. Physical Review E47, 2155–2161 (1993)
Litinskii, L.B.: Direct calculation of the stable points of a neural network. Theoretical and Mathematical Physics 101(3), 1492–1501 (1994)
Xu, R., Wunsh II, D.: Survey of Clustering Algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)
Li, T., Zhu, S., Ogihara, M.: Algorithms for clustering high dimensional and distributed data. Intelligent Data Analysis 7, 305–326 (2003)
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© 2007 Springer-Verlag Berlin Heidelberg
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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
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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
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