The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 45–53 | Cite as

Selection of recurrence threshold for signal detection

Article

Abstract

Over the last years recurrence plots (RPs)and recurrence quantification analysis (RQA)have become quite popular in various branches of science. One key problem in applying RPs and RQA is the selection of suitable parameters for the data under investigation. Whereas various well-established methods for the selection of embedding parameters exists, the question of choosing an appropriate threshold has not yet been answered satisfactorily. The recommendations found in the literature are rather rules of thumb than actual guidelines. In this paper we address the issue of threshold selection in RP/RQA. The core criterion for choosing a threshold is the power in signal detection that threshold yields. We will validate our approach by applying it to model as well as real-life data.

Keywords

European Physical Journal Special Topic Receiver Operating Characteristic Receiver Operating Characteristic Curve Recurrence Plot Phase Space Trajectory 

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References

  1. T. Aparicio, E.F. Pozo, D. Saura, J. Econom. Behav. Org. 65, 768 (2008) Google Scholar
  2. L. Cao, Physica D 110, 43 (1997) Google Scholar
  3. T. Fawcett, Patt. Recogn. Lett. 27, 861 (2006) Google Scholar
  4. A.M. Fraser, H.L. Swinney, Phys. Rev. A 33, 1134 (1986) Google Scholar
  5. J.B. Gao, H.Q. Cai, Phys. Lett. A 270, 75 (2000) Google Scholar
  6. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis (University Press, Cambridge, 1997) Google Scholar
  7. M. Koebbe, G. Mayer-Kress, Proceedings of SFI Studies in the Science of Complexity, edited by M. Casdagli, S. Eubank, Vol. 21 (Redwood City, Addison-Wesley, 1992), p. 361 Google Scholar
  8. N. Marwan, A. Groth, J. Kurths, Chaos Complex. Lett. 2, 301 (2007) Google Scholar
  9. N. Marwan, J. Kurths, Rohde et al., Physica D 237, 619 (2008); Physica D (submitted) Google Scholar
  10. N. Marwan, A. Meinke, Int. J. Bifurc. Chaos 14, 761 (2004) Google Scholar
  11. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007) Google Scholar
  12. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Phys. Rev. E 66, 026702 (2002) Google Scholar
  13. G.M. Mindlin, R. Gilmore, Physica D 58, 229 (1992) Google Scholar
  14. G.K. Rohde, J.M. Nichols, B.M. Dissinger, F. Bucholtz, Physica D 237, 619 (2008) Google Scholar
  15. M.C. Romano, M. Thiel, J. Kurths, I.Z. Kiss, J. Hudson, Europhys. Lett. 71, 466 (2005) Google Scholar
  16. S. Schinkel, N. Marwan, J. Kurths, Cognit. Neurodyn. 1, 317 (2007) Google Scholar
  17. S. Sutton, M. Braren, J. Zubin, E.R. John, Science 150, 1187 (1965) Google Scholar
  18. M. Thiel, M.C. Romano, J. Kurths, R. Meucci, E. Allaria, F.T. Arecchi, Physica D 171, 138 (2002) Google Scholar
  19. A.A. Tsonis, Int. J. Bifurc. Chaos 17, 4229 (2007) Google Scholar
  20. A. Venkatesan, M. Lakshmanan, Phys. Rev. E 63, 026219 (2001) Google Scholar
  21. J.P. Zbilut, A. Giuliani, C.L. Webber Jr., Phys. Lett. A 267, 1742 (2000) Google Scholar
  22. J.P. Zbilut, A. Giuliani, C.L. Webber Jr., Phys. Lett. A 246, 122 (1998) Google Scholar
  23. J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 171, 199 (1992) Google Scholar
  24. J.P. Zbilut, J.-M. Zaldívar-Comenges, F. Strozzi, Phys. Lett. A 297, 173 (2002) Google Scholar
  25. M.H. Zweig, G. Campbell, Clin. Chem. 39, 561 (1993) Google Scholar
  26. M. Valsecchi, O. Dimigen, R. Kliegl, W. Sommer, M. Turratto (accepted) Google Scholar

Copyright information

© EDP Sciences and Springer 2008

Authors and Affiliations

  1. 1.Interdisciplinary Centre for Dynamics of Complex Systems, University of PotsdamPotsdamGermany
  2. 2.Department of PsychologyUniversity of PotsdamPotsdamGermany
  3. 3.Potsdam Institute for Climate Impact Research (PIK)PotsdamGermany

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