The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Permutation Entropy: A Natural Complexity Measure for Time Series
Abstract
We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations.
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Cites
Ergodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
Cornfeld, I. P., Sinaǐ, Y. G., & Fomin, S. (1982) · Cited by 2,852
Digital processing of speech signals
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Digital Processing of Speech Signals
Ackroyd, M. H. (1979) · Electronics and Power · doi:10.1049/ep.1979.0173 · Cited by 2,391
Analysis of Observed Chaotic Data
Abarbanel, H. D. I., & Gollub, J. P. (1996) · Physics Today · doi:10.1063/1.881528 · Cited by 1,821
Iterated Maps on the Interval as Dynamical Systems
Collet, P., & Eckmann, J.-P. (2009) · Birkhäuser Boston eBooks · doi:10.1007/978-0-8176-4927-2 · Cited by 1,647
Estimation of the Kolmogorov entropy from a chaotic signal
Grassberger, P., & Procaccia, I. (1983) · Physical Review A · doi:10.1103/physreva.28.2591 · Cited by 1,440
Analysis of Observed Chaotic Data
Abarbanel, H. D. I. (1996) · Institute for Nonlinear Science · doi:10.1007/978-1-4612-0763-4 · Cited by 1,189
Dimension Theory in Dynamical Systems: Contemporary Views and Applications
Pesin, Y. B. (1997) · University of Chicago Press eBooks · doi:10.7208/chicago/9780226662237.001.0001 · Cited by 940
Petersen, K. E. (1983) · Cambridge University Press eBooks · doi:10.1017/cbo9780511608728 · Cited by 492
Cited by
Distinguishing Noise from Chaos
Rosso, O. A., Larrondo, H. A., Martin, M. T., Plastino, A., & Fuentes, M. A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.154102 · Cited by 710
Sitt, J. D., King, J.-R., El Karoui, I., Rohaut, B., Faugeras, F., Gramfort, A., Cohen, L., Sigman, M., Dehaene, S., & Naccache, L. (2014) · Brain · doi:10.1093/brain/awu141 · Cited by 608
Zhang, X., Liang, Y., Zhou, J., & zang, Y. (2015) · Measurement · doi:10.1016/j.measurement.2015.03.017 · Cited by 586
Information Sharing in the Brain Indexes Consciousness in Noncommunicative Patients
King, J.-R., Sitt, J. D., Faugeras, F., Rohaut, B., El Karoui, I., Cohen, L., Naccache, L., & Dehaene, S. (2013) · Current Biology · doi:10.1016/j.cub.2013.07.075 · Cited by 370
Schartner, M., Seth, A., Noirhomme, Q., Boly, M., Bruno, M.-A., Laureys, S., & Barrett, A. (2015) · PLOS ONE · doi:10.1371/journal.pone.0133532 · Cited by 287
“In support of this, simple randomness measures applicable to a single time series, such as approximate entropy [52] and permutation entropy [31], have been found to decrease during anaesthesia and sleep [27, 28, 32, 34].”
Method
Metadata
- Authors
- Bandt, C., & Pompe, B.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-04-11
- Volume
- 88
- Issue
- 17
- Pages
- 174102-174102
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2014683958
- Cited by
- 4,867
- References
- 13
- FWCI
- 4.39
- Type
- journal article
- Language
- en
- Open access
- closed
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- Bandt, C., & Pompe, B. (2002). Permutation Entropy: A Natural Complexity Measure for Time Series. Physical Review Letters. https://doi.org/10.1103/physrevlett.88.174102
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
