Skip to main content

Nonlinear Time Series Analysis by Using Gamma Growing Neural Gas

  • Conference paper
Advances in Self-Organizing Maps

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 198))

Abstract

In this paper, we investigate the properties of the Gamma Growing Neural Gas (γ-GNG) model for the analysis of nonlinear time series. This model includes a temporal context descriptor based on a short term memory structure called Gamma memory. It is shown that γ-GNG can approximately reconstruct the space-state, and filter out additive noise. Simulation results on two data sets are presented: Lorenz system and NH3-FIR Laser time series.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)

    Book  Google Scholar 

  2. Voegtlin, T.: Recursive Self-Organizing Maps. Neural Networks 15, 979–991 (2002)

    Article  Google Scholar 

  3. Hammer, B., Micheli, A., Sperduti, A., Strickert, M.: Recursive Self-Organizing Network Models. Neural Networks 17, 1061–1085 (2004)

    Article  MATH  Google Scholar 

  4. Strickert, M., Hammer, B.: Merge SOM for Temporal Data. Neurocomputing 64, 39–72 (2005)

    Article  Google Scholar 

  5. Martinetz, T.M., Berkovich, S.G., Schulten, K.J.: “Neural-gas” Network for Vector Quantization and its Application to Time-Series Prediction. IEEE Transactions on Neural Networks, 558–569 (1993)

    Google Scholar 

  6. Fritzke, B.: A Growing Neural Gas Learns Topologies. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) Neural Information Processing Systems (NIPS), pp. 625–632. MIT Press, Cambridge (1995)

    Google Scholar 

  7. Strickert, M., Hammer, B.: Neural Gas for Sequences. In: Yamakawa, T. (ed.) Proceedings of the Workshop on Self-Organizing Networks (WSOM), Kyushu, Japan, pp. 53–58 (2003)

    Google Scholar 

  8. Andreakis, A., Hoyningen-Huene, N.v., Beetz, M.: Incremental Unsupervised Time Series Analysis Using Merge Growing Neural Gas. In: Príncipe, J.C., Miikkulainen, R. (eds.) WSOM 2009. LNCS, vol. 5629, pp. 10–18. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. De Vries, B., Principe, J.C.: The Gamma Model- A New Neural Model for Temporal Processing. Neural Networks 5, 565–576 (1992)

    Article  Google Scholar 

  10. Estévez, P.A., Hernández, R.: Gamma SOM for Temporal Sequence Processing. In: Príncipe, J.C., Miikkulainen, R. (eds.) WSOM 2009. LNCS, vol. 5629, pp. 63–71. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Estévez, P.A., Hernández, R., Perez, C.A., Held, C.M.: Gamma-filter Self-organizing Neural Networks for Unsupervised Sequence Processing. Electronics Letters 47(8), 494–496 (2011)

    Article  Google Scholar 

  12. Estévez, P.A., Hernández, R.: Gamma-Filter Self-Organizing Neural Networks for Time Series Analysis. In: Laaksonen, J., Honkela, T. (eds.) WSOM 2011. LNCS, vol. 6731, pp. 151–159. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Takens, F.: Detecting Strange Atractors in Turbulence. Lecture Notes in Math., vol. 898. Springer, New York (1981)

    Google Scholar 

  14. Sauer, T.: Times series prediction using delay coordinate embedding. In: Weigend, A.S., Gershenfeld, N.A. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past, pp. 175–193. Addison-Wesley, FL (1994)

    Google Scholar 

  15. Fraser, A.M., Swinney, H.L.: Independent Coordinates for Strange Attractors from Mutual Information. Physical Review A 33, 1134–1140 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction. Physical Review A 45, 3403–3411 (1992)

    Article  Google Scholar 

  17. Bradley, E.: Analysis of Time Series. In: Berthold, M., Hand, D.J. (eds.) Intelligent Data Analysis. Springer, Berlin (1999)

    Google Scholar 

  18. Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, New York (2004)

    MATH  Google Scholar 

  19. Principe, J.C., Giuliano, N.R., Lefebvre, W.C.: Neural and Adaptive Systems. John Wiley & Sons, Inc., New York (1999)

    Google Scholar 

  20. Lorenz, E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130 (1963)

    Article  Google Scholar 

  21. Huebner, U., Weiss, C.O., Abraham, N.B., Tang, D.: Lorenz-like Chaos in NH3-FIR Lasers (Data Set A). In: Weigend, A.S., Gershenfeld, N.A. (eds.) Time Series Prediction: Forecasting the Future and Understanding the Past, pp. 73–104. Addison-Wesley, FL (1994)

    Google Scholar 

  22. M.N., Romano, M.C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems. Physics Reports 438, 237–329 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pablo A. Estévez .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Estévez, P.A., Vergara, J.R. (2013). Nonlinear Time Series Analysis by Using Gamma Growing Neural Gas. In: Estévez, P., Príncipe, J., Zegers, P. (eds) Advances in Self-Organizing Maps. Advances in Intelligent Systems and Computing, vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35230-0_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35230-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35229-4

  • Online ISBN: 978-3-642-35230-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics