The Journal of Supercomputing

, Volume 75, Issue 3, pp 1175–1186 | Cite as

Highly scalable algorithm for computation of recurrence quantitative analysis

  • Tomáš MartinovičEmail author
  • Georg Zitzlsberger


Recurrence plot analysis is a well-established method to analyse time series in numerous areas of research. However, it has exponential computational and spatial complexity. As the main result of this paper, a technique for the computation of recurrence quantitative analysis (RQA) is outlined. This method significantly reduces spatial complexity of computation by computing RQA directly from the time series, optimizing memory accesses and reducing computational time. Additionally, parallel implementation of this technique is tested on the Salomon cluster and is proved to be extremely fast and scalable. This means that recurrence quantitative analysis may be applied to longer time series or in applications with the need of real-time analysis.


Recurrence quantitative analysis Recurrence plot Algorithms Time series High-performance computing 



This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science - LQ1602” and by the IT4Innovations infrastructure which is supported from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center LM2015070”. This work was partially supported by grant of SGS No. SP2017/182 “Solving graph problems on spatio-temporal graphs with uncertainty using HPC”, VŠB - Technical University of Ostrava, Czech Republic.


  1. 1.
    Acharya UR, Sree SV, Chattopadhyay S, Yu W, Ang PCA (2011) Application of recurrence quantification analysis for the automated identification of epileptic EEG signals. Int J Neural Syst 21(3):199–211.
  2. 2.
    Balibrea F (2016) On problems of topological dynamics in non-autonomous discrete systems. Appl Math Nonlinear Sci 1(2):391–404.
  3. 3.
    Bradley E, Kantz H (2015) Nonlinear time-series analysis revisited. Chaos 25(9):097610. arXiv:1503.07493 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Builes-Jaramillo A, Marwan N, Poveda G, Kurths J (2017) Nonlinear interactions between the Amazon river basin and the tropical North Atlantic at interannual timescales. Clim Dyn. Google Scholar
  5. 5.
    Center INS (2015) Salomon cluster.
  6. 6.
    Firooz SG, Almasganj F, Shekofteh Y (2017) Improvement of automatic speech recognition systems via nonlinear dynamical features evaluated from the recurrence plot of speech signals. Comput Electr Eng 58:215–226.
  7. 7.
    Flake GW (1998) The computational beauty of nature computer explorations of fractals, chaos, complex systems, and adaptation. MIT Press, CambridgezbMATHGoogle Scholar
  8. 8.
    Forum MP (1994) MPI: a message-passing interface standard. Tech. Rep., Univerisity of Tennessee, Knoxville, TN, USAGoogle Scholar
  9. 9.
    Fousse L, Hanrot G, Lefèvre V, Pélissier P, Zimmermann P (2007) MPFR: a multiple-precision binary floating-point library with correct rounding. ACM Trans Math Softw. MathSciNetzbMATHGoogle Scholar
  10. 10.
    Fukino M, Hirata Y, Aihara K (2016) Coarse-graining time series data: recurrence plot of recurrence plots and its application for music. Chaos Interdiscip J Nonlinear Sci 26(2):023,116. MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hemakom A, Chanwimalueang T, Carrin A, Aufegger L, Constantinides AG, Mandic DP (2016) Financial stress through complexity science. IEEE J Sel Topics Signal Process 10(6):1112–1126. CrossRefGoogle Scholar
  12. 12.
    Hermann S (2005) Exploring sitting posture and discomfort using nonlinear analysis methods. IEEE Trans Inf Technol Biomed 9(3):392–401. CrossRefGoogle Scholar
  13. 13.
    Karain WI, Qaraeen NI (2017) The adaptive nature of protein residue networks. Proteins Struct Funct Bioinform 85(5):917–923. CrossRefGoogle Scholar
  14. 14.
    Lampart M, Martinovič T (2017) A survey of tools detecting the dynamical properties of one-dimensional families. Adv Electr Electron Eng 15(2):304–313.
  15. 15.
    Lancia L, Voigt D, Krasovitskiy G (2016) Characterization of laryngealization as irregular vocal fold vibration and interaction with prosodic prominence. J Phon 54:80–97.
  16. 16.
    Manuca R, Savit R (1996) Stationarity and nonstationarity in time series analysis. Physica D Nonlinear Phenom 99(2):134–161.
  17. 17.
    Martinovič T, Zitzlsberger G (2017) Rqa_hpc.
  18. 18.
    Marwan N, Romano MC, Thiel M, Kurths J (2007) Recurrence plots for the analysis of complex systems. Phys Rep 438(5):237–329.
  19. 19.
    Meng HB, Song MY, Yu Y-F, Wu J-H (2016) Recurrence quantity analysis of the instantaneous pressure fluctuation signals in the novel tank with multi-horizontal submerged jets. Chem Biochem Eng Q 30(1):19–31. CrossRefGoogle Scholar
  20. 20.
    Mesin E, Monaco A, Cattaneo R (2013) Investigation of nonlinear pupil dynamics by recurrence quantification analysis. BioMed Res Int. Google Scholar
  21. 21.
    Nalband S, Sundar A, Prince AA, Agarwal A (2016) Feature selection and classification methodology for the detection of knee-joint disorders. Comput Methods Programs Biomed 127:94–104.
  22. 22.
    Olyaee MH, Yaghoubi A, Yaghoobi M (2016) Predicting protein structural classes based on complex networks and recurrence analysis. J Theor Biol 404:375–382.
  23. 23.
    Rawald T, Sips M, Marwan N, Dransch D (2014) Fast computation of recurrences in long time series. Springer, Cham, pp 17–29. Google Scholar
  24. 24.
    Rawald T, Sips M, Marwan N (2017) Pyrqaconducting recurrence quantification analysis on very long time series efficiently. Comput Geosci 104:101–108.
  25. 25.
    Spiegel S, Jain JB, Albayrak S (2014) A recurrence plot-based distance measure. Springer, Cham, pp 1–15. Google Scholar
  26. 26.
    Spiegel S, Schultz D, Marwan N (2016) Approximate recurrence quantification analysis (aRQA) in code of best practice. Springer, Cham, pp 113–136. Google Scholar
  27. 27.
    Takens F (1981) Detecting strange attractors in turbulence. Springer, Berlin, pp 366–381. zbMATHGoogle Scholar
  28. 28.
    Webber CL, Zbilut JP (1994) Dynamical assessment of physiological systems and states using recurrence plot strategies. J Appl Physiol 76(2):965–973.
  29. 29.
    Zbilut JP, Webber CL (1992) Embeddings and delays as derived from quantification of recurrence plots. Phys Lett A 171(3):199–203.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IT4Innovations, VŠB – Technical University of OstravaOstrava–PorubaCzech Republic

Personalised recommendations