Efficient Pattern Recognition Using the Frequency Response of a Spiking Neuron

  • Sergio Valadez-Godínez
  • Javier González
  • Humberto SossaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10267)


In previous works, a successful scheme using a single Spiking Neuron (SN) to solve complex problems in pattern recognition has been proposed. This consists in using the firing frequency response to classify a given input pattern, which is multiplied by a weight vector to produce a constant stimulation current. The weight vector is adjusted by an evolutionary strategy where the objective is to obtain an optimal frequency separation. The problem is that the SN has to be numerically simulated several times when the weight vector is being adjusted. In this work, we propose fitting the SN frequency response curve to a piecewise linear function to be used instead of the costly SN simulation. A high fitting degree was found, but, more importantly, the computational cost of the training and testing phases was drastically reduced.


Spiking Neuron Izhikevich Pattern recognition Curve fitting Frequency Response Curve Piecewise linear function Firing Rate Evolutionary strategy Differential evolution Computational cost 



S. Valadez-Godínez would like to thank CONACYT and SIP-IPN for the scholarship granted in pursuit of his doctoral studies. J. González would like to thank CONACYT and SIP-IPN for undertaking his Master studies. H. Sossa would like to thank SIP-IPN and CONACYT under grants 20170693 and 65 (Frontiers of Science) to carry out this research. We are also very grateful to reviewers for their helpful comments.


  1. 1.
    Vazquez, R.A., Cachón, A.: Integrate and Fire neurons and their application in pattern recognition. In: 7th International Conference on Electrical Engineering Computing Science and Automatic Control, pp. 424–428 (2010)Google Scholar
  2. 2.
    Vazquez, R.: Izhikevich neuron model and its application in pattern recognition. Aust. J. Intell. Inform. Process. Syst. 11, 35–40 (2010)Google Scholar
  3. 3.
    Vázquez, R.A.: Pattern recognition using spiking neurons and firing rates. In: Kuri-Morales, A., Simari, G.R. (eds.) IBERAMIA 2010. LNCS, vol. 6433, pp. 423–432. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16952-6_43 CrossRefGoogle Scholar
  4. 4.
    Vazquez, R.A.: Training spiking neural models using cuckoo search algorithm. In: 2011 IEEE Congress of Evolutionary Computation (CEC), pp. 679–686 (2011)Google Scholar
  5. 5.
    Vázquez, R.A., Garro, B.A.: Training spiking neurons by means of particle swarm optimization. In: Tan, Y., Shi, Y., Chai, Y., Wang, G. (eds.) ICSI 2011. LNCS, vol. 6728, pp. 242–249. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-21515-5_29 CrossRefGoogle Scholar
  6. 6.
    Matadamas Ortiz, I.C.: Aplicación de las Redes Neuronales Pulsantes en el reconocimiento de patrones y análisis de imágenes. Master’s thesis, Instituto Politécnico Nacional, Centro de Investigación en Computación, México (2014)Google Scholar
  7. 7.
    Vazquez, R.A., Garro, B.A.: Training spiking neural models using artificial bee colony. Comput. Intell. Neurosci. 2015, 14 (2015). Article ID 947098CrossRefGoogle Scholar
  8. 8.
    Carino-Escobar, R.I., Cantillo-Negrete, J., Gutierrez-Martinez, J., Vazquez, R.A.: Classification of motor imagery electroencephalography signals using spiking neurons with different input encoding strategies. Neural Comput. Appl., 1–13 (2016)Google Scholar
  9. 9.
    Minsky, M., Papert, S.: Perceptrons: An Introduction to Computational Geometry. The MIT Press, Cambridge (1969)zbMATHGoogle Scholar
  10. 10.
    Adrian, E.D.: The Basis of Sensation. The Action of the Sense Organs. Christophers, London (1928)Google Scholar
  11. 11.
    Lapicque, M.L.: Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation. J. Physiol. Pathol. Gen. 9, 620–635 (1907)Google Scholar
  12. 12.
    Stein, R.B.: A theoretical analysis of neuronal variability. Biophys. J. 5, 173–194 (1965)CrossRefGoogle Scholar
  13. 13.
    Izhikevich, E.M.: Simple model of spiking neurons. IEEE Trans. Neural Netw. 14, 1569–1572 (2003)CrossRefGoogle Scholar
  14. 14.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)CrossRefGoogle Scholar
  15. 15.
    Agin, D.: Hodgkin-Huxley equations: logarithmic relation between membrane current and frequency of repetitive activity. Nature 201, 625–626 (1964)CrossRefGoogle Scholar
  16. 16.
    Storn, R., Price, K.: Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  18. 18.
    Yang, X.S., Deb, S.: Cuckoo search via lévy flights. In: 2009 World Congress on Nature Biologically Inspired Computing (NaBIC), pp. 210–214 (2009)Google Scholar
  19. 19.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks Proceedings, vol. 4, pp. 1942–1948 (1995)Google Scholar
  20. 20.
    Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)Google Scholar
  21. 21.
    Krinskii, V.I., Kokoz, Y.M.: Analysis of equations of excitable membranes - I. Reduction of the Hodgkin-Huxley equations to a second order system. Biofizika, pp. 506–511 (1973)Google Scholar
  22. 22.
    Kepler, T.B., Abbott, L.F., Marder, E.: Reduction of conductance-based neuron models. Biol. Cybern. 66, 381–387 (1992)CrossRefzbMATHGoogle Scholar
  23. 23.
    Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press, Cambridge (2007)Google Scholar
  24. 24.
    Euler, L.: Institutionum calculi integralis. Volumen primum. Petropoli: Impenfis Academiae Imperialis Scientiarum (1768)Google Scholar
  25. 25.
    Humphries, M.D., Gurney, K.: Solution methods for a new class of simple model neurons. Neural Comput. 19, 3216–3225 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Skocik, M.J., Long, L.N.: On the capabilities and computational costs of neuron models. IEEE Trans. Neural Netw. Learn. Syst. 25, 1474–1483 (2014)CrossRefGoogle Scholar
  27. 27.
    MATLAB: Version 8.5.0 (R2015a). The MathWorks Inc., Natick, Massachusetts (2015)Google Scholar
  28. 28.
    Lichman, M.: UCI machine learning repository (2013)Google Scholar
  29. 29.
    Alpayd, E.: Introduction to Machine Learning. Second edn. The MIT Press (2010)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sergio Valadez-Godínez
    • 1
  • Javier González
    • 1
  • Humberto Sossa
    • 1
    Email author
  1. 1.Centro de Investigación en ComputaciónInstituto Politécnico NacionalMexico CityMexico

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