Approximation of diagonal line based measures in recurrence quantification analysis

Schultz, David; Spiegel, Stephan; Marwan, Norbert; Albayrak, Şahin

doi:10.1016/j.physleta.2015.01.033

Cited by 28 publications

(28 citation statements)

References 26 publications

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“…In earlier work [17] we have proven the equivalence between our alternative and the original formulation of the RQA measures and, furthermore, analyzed the approximation error theoretically. Moreover, we have provided detailed information on the discretization and employed algorithms [17], which have complexity of (N log(N)).…”

Section: Approximate Recurrence Quantification Analysismentioning

confidence: 80%

“…Given a time series with about one million data points, distributed computing with two GPUs has been shown to reduce the RQA calculation time by 1-2 orders of magnitude [16]. However, this work demonstrates that the proposed approximations [17] are able to reduce the RQA calculation time (for the same one million measurements) by 4 orders of magnitude. This tremendous speedup makes the approximation approach extremely valuable for many real-life data analysis tasks, although it does not yield exact results.…”

Section: Introductionmentioning

confidence: 81%

“…Since the quantification of recurring patterns is computational expensive, speedup techniques [16] and approximations [17] have been proposed. Speedup techniques commonly use distributed computing that ensures exact RQA results, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In this work we extend the approximation approach [17] to vertical line based measures, assess the runtime of our approximate RQA measures for relatively long time series (from climate impact research), and investigate the use our approximate RQA measures for transition detection.…”

Section: Introductionmentioning

confidence: 99%

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Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice

Spiegel

Schultz

Marwan

2016

Springer Proceedings in Physics

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Recurrence quantification analysis (RQA) is a well-known tool for studying nonlinear behavior of dynamical systems, e.g. for finding transitions in climate data or classifying reading abilities. But the construction of a recurrence plot and the subsequent quantification of its small and large scale structures is computational demanding, especially for long time series or data streams with high sample rate. One way to reduce the time and space complexity of RQA are approximations, which are sufficient for many data analysis tasks, although they do not guarantee exact solutions. In earlier work, we proposed how to approximate diagonal line based RQA measures and showed how these approximations perform in finding transitions for difference equations. The present work aims at extending these approximations to vertical line based RQA measures and investigating the runtime/accuracy of our approximate RQA measures on real-life climate data. Our empirical evaluation shows that the proposed approximate RQA measures achieve tremendous speedups without losing much of the accuracy.

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Section: Approximate Recurrence Quantification Analysismentioning

confidence: 80%

Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice

Spiegel

Schultz

Marwan

2016

Springer Proceedings in Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such quantification is important since it will be employed to characterize the dynamical information and to perform predictions. These statistical measures are known as Recurrence Quantification Analysis (RQA) and are based on the density of recurrence points, the diagonal and vertical line structures in the RP [21,23,24]. RQA can be applied to non-stationary processes in continuous or discrete time series.…”

Section: Recurrence Quantification Analysismentioning

confidence: 99%