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Efficient computation of recurrence quantification analysis via microstates

Author

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  • Froguel, Lucas Belasque
  • de Lima Prado, Thiago
  • Corso, Gilberto
  • dos Santos Lima, Gustavo Zampier
  • Lopes, Sergio Roberto

Abstract

Recurrence plot (RP) is a powerful tool in the study of nonlinear dynamics, being successfully applied in economics, medicine, geophysics, and astronomy. The Recurrence Quantification Analysis (RQA) consists of a methodology to compute RP quantifiers based on statistics over vertical/diagonal recurrent lines, densities, and other features of the RP. The traditional way to calculate the quantifiers computes each recurrent point individually and builds the histogram of the whole RP. Here we propose a new, statistical approach to calculate the quantifiers using the (recurrence) microstates, which are small representative chunks of the RP. The new way of statistically calculating the quantifiers converges fast and brings a computational gain. In particular, it reduces the time complexity from O(K2) to O(K), for K the size of the time-series. Moreover, we show that our results are independent of the system and series size.

Suggested Citation

  • Froguel, Lucas Belasque & de Lima Prado, Thiago & Corso, Gilberto & dos Santos Lima, Gustavo Zampier & Lopes, Sergio Roberto, 2022. "Efficient computation of recurrence quantification analysis via microstates," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322002491
    DOI: 10.1016/j.amc.2022.127175
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    References listed on IDEAS

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