Abstract
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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References
N. Marwan, A historical review of recurrence plots. Eur. Phys. J. Spec. Topics 164(1), 3–12 (2008)
C.L. Webber Jr., N. Marwan, A. Facchini, A. Giuliani, Simpler methods do it better: success of recurrence quantification analysis as a general purpose data analysis tool. Phys. Lett. A 373, 3753–3756 (2009)
S. Spiegel, J.B. Jain, S. Albayrak, A Recurrence Plot-Based Distance Measure, vol. 103 (Springer, Cham, 2014), pp. 1–15
S. Spiegel, D. Schultz, S. Albayrak, BestTime: Finding representatives in time series datasets. Lecture Notes in Computer Science: Artificial Intelligence, vol. 8726, pp. 477–480 (2014)
F. Hasselman, Classifying acoustic signals into phoneme categories: average and dyslexic readers make use of complex dynamical patterns and multifractal scaling properties of the speech signal. PeerJ 3, e837 (2015)
M.A.F. Harrison, M.G. Frei, I. Osorio, Detection of seizure rhythmicity by recurrences. Chaos 18(3), 033124 (2008)
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Recurrence plot based measures of complexity and its application to heart rate variability data. Phys. Rev. E 66(2), 026702 (2002)
A. Giuliani, M. Tomasi, Recurrence quantification analysis reveals interaction partners in paramyxoviridae envelope glycoproteins. Proteins: Struct. Func. Genetics 46(2), 171–176 (2002)
S. Spiegel, Discovery of Driving Behavior Patterns (Springer, Cham, 2015), pp. 315–343
N. Marwan, S. Schinkel, J. Kurths, Recurrence plots 25 years later: gaining confidence in dynamical transitions. Europhys. Lett. 101, 20007 (2013)
J.F. Donges, R.V. Donner, M.H. Trauth, N. Marwan, H.J. Schellnhuber, J. Kurths, Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution. Proc. Natl. Acad. Sci. 108(51), 20422–20427 (2011)
G. Litak, A.K. Sen, A. Syta, Intermittent and chaotic vibrations in a regenerative cutting process. Chaos Solitons Fractals 41(4), 2115–2122 (2009)
M.C. Romano, M. Thiel, J. Kurths, I.Z. Kiss, J. Hudson, Detection of synchronization for non-phase-coherent and non-stationary data. Europhys. Lett. 71(3), 466–472 (2005)
Y. Hirata, K. Aihara, Identifying hidden common causes from bivariate time series: a method using recurrence plots. Phys. Rev. E 81(1), 016203 (2010)
J.H. Feldhoff, R.V. Donner, J.F. Donges, N. Marwan, J. Kurths, Geometric signature of complex synchronisation scenarios. Europhys. Lett. 102(3), 30007 (2013)
T. Rawald, M. Sips, N. Marwan, D. Dransch, Fast Computation of Recurrences in Long Time Series, vol. 103 (Springer, Cham, 2014), pp. 17–29
D. Schultz, S. Spiegel, N. Marwan, S. Albayrak, Approximation of diagonal line based measures in recurrence quantification analysis. Phys. Lett. A 379(14–15), 997–1011 (2015)
J.-P. Eckmann, S. Oliffson, Kamphorst, D. Ruelle, Recurrence plots of dynamical systems. Europhys. Lett. 4(9), 973–977 (1987)
N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Geometry from a time series. Phys. Rev. Lett. 45(9), 712–716 (1980)
N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5–6), 237–329 (2007)
J.P. Zbilut, C.L. Webber Jr., Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171(3–4), 199–203 (1992)
C.L. Webber Jr., J.P. Zbilut, Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76(2), 965–973 (1994)
M. Thiel, M.C. Romano, P.L. Read, J. Kurths, Estimation of dynamical invariants without embedding by recurrence plots. Chaos 14(2), 234–243 (2004)
N. Marwan, J.F. Donges, Y. Zou, R.V. Donner, J. Kurths, Complex network approach for recurrence analysis of time series. Phys. Lett. A 373(46), 4246–4254 (2009)
T. Rawald, pyRQA (2015)
M. Scheffer, J. Bascompte, W.A. Brock, V. Brovkin, S.R. Carpenter, V. Dakos, H. Held, E.H. van Nes, M. Rietkerk, G. Sugihara, Early-warning signals for critical transitions. Nature 461(7260), 53–59 (2009)
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Spiegel, S., Schultz, D., Marwan, N. (2016). Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice. In: Webber, Jr., C., Ioana, C., Marwan, N. (eds) Recurrence Plots and Their Quantifications: Expanding Horizons. Springer Proceedings in Physics, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-319-29922-8_6
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DOI: https://doi.org/10.1007/978-3-319-29922-8_6
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