Computing the Weights of Polynomial Cellular Neural Networks Using Quadratic Programming

  • Anna Rubi-Velez
  • Eduardo Gomez-Ramirez
  • Giovanni E. Pazienza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5856)


Finding the weights of a Polynomial Cellular Neural/Nonlinear Network performing a given task is not straightforward. Several approaches have been proposed so far, but they are often computationally expensive. Here, we prove that quadratic programming can solve this problem efficiently and effectively in the particular case of a totalistic network. Besides the theoretical treatment, we present several examples in which our method is employed successfully for any complexity index.


polynomial cellular neural networks cellular automata quadratic programming 


  1. 1.
    Chua, L.O., Yang, L.: Cellular neural networks: Theory and Applications. IEEE Trans. Circuits Syst. 35, 1257–1290 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    von Neumann, J.: The general and logical theory of automata. In: Jeffress, L.A. (ed.) Cerebral Mechanisms in Behavior–The Hixon Symposium. s.l. John Wiley, Chichester (1951)Google Scholar
  3. 3.
    Chua, L.O., Yook, S., Dogaru, R.: A nonlinear dynamics perspective of Wolfram’s new kind of science. Part I: Threshold of complexity. International Journal of Bifurcation and Chaos 12, 2655–2766 (2002)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dogaru, R., Chua, L.O.: Universal CNN cells. International Journal of Bifurcation and Chaos 9(1), 1–48 (1999)zbMATHCrossRefGoogle Scholar
  5. 5.
    Pazienza, G.E., Gomez-Ramirez, E.y., Vilasis-Cardona, X.: Portugal Polynomial discrete time cellular neural networks for implementing the Game of Life.: s.n. In: Proc. International Conference on Artificial Neural Networks, ICANN 2007 (2007)Google Scholar
  6. 6.
    Giovanni, E., Gomez-Ramirez, E.: New properties of 2D Cellular Automata found through Polynomial Cellular Neural Network. In: International Joint Conference on Neural Networks (IJCNN 2009), Pazienza, Atlanta, USA (2009)Google Scholar
  7. 7.
    Schonmeyer, D., Feiden, D., Tetzlaff, R.: Multi-template training for image processing with cellular neural networks. In: Proc. of 2002 7th IEEE International Workshop on Cellular Neural Networks and their Applications (CNNA 2002), Frankfurt, Germany (2002)Google Scholar
  8. 8.
    Pazienza, G., Gomez-Ramirez, E., Vilasis-Cardona, E.: Polynomial discrete time cellular neural networks to solve the XOR problem. In: Proc. 10th International Workshop on Cellular Neural Networks and ther Applications (CNNA 2006), X. Istanbul, Turkey (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Anna Rubi-Velez
    • 1
  • Eduardo Gomez-Ramirez
    • 2
  • Giovanni E. Pazienza
    • 3
  1. 1.Enginyeria i Arquitectura La SalleUniversitat Ramon LlullBarcelonaSpain
  2. 2.LIDETEA, Posgrado e InvestigacionUniversidad La SalleMexico CityMexico
  3. 3.Cellular Sensory and Wave Computing LaboratoryMTA-SZTAKIBudapestHungary

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