Permutation entropy: a natural complexity measure for time series.

@article{Bandt2002PermutationEA,
  title={Permutation entropy: a natural complexity measure for time series.},
  author={Christoph Bandt and Bernd Pompe},
  journal={Physical review letters},
  year={2002},
  volume={88 17},
  pages={
          174102
        }
}
  • C. BandtB. Pompe
  • Published 11 April 2002
  • Computer Science
  • Physical review letters
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… 

Figures from this paper

Easily adaptable complexity measure for finite time series.

  • Da-guan KeQinye Tong
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the widely accepted but conflicting criteria for complexity measurements.

Permutation entropy as a tool for analyzing noise-like time series

The subject of this work is the study of time series of fluctuations or noise-like time series, where it is believed that locally such time series are completely random and do not carry any information.

Characterizing time series via complexity-entropy curves.

A family of complexity measures for time series based on a generalization of the complexity-entropy causality plane is proposed and it is proved that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.

ENTROPY DETERMINATION BASED ON THE ORDINAL STRUCTURE OF A DYNAMICAL SYSTEM

The theory of determining the Kolmogorov-Sinai entropy of a measure-preserving dynamical system via increasing sequences of order generated partitions of the state space is summarized and generalized.

Permutation Entropies and Chaos

Permutation entropy is a metric used to quantify the regularity of a time series. Here I report on its application to the problem of characterizing the behavior of a few nonlinear dynamical systems,

Increment Entropy as a Measure of Complexity for Time Series

Simulations on synthetic data and tests on epileptic electroencephalogram (EEG) signals demonstrate an increment entropy's ability of detecting abrupt changes, regardless of the energetic (e.g., spikes or bursts) or structural changes.

Parameter Selection for Permutation Entropy Measurements

We investigate the applicability of the permutation entropy H and a synchronization index γ that is based on the changing tendency of temporal permutation entropies to analyze noisy time series from

Informational Time Causal Planes: A Tool for Chaotic Map Dynamic Visualization

A bidimensional plane is constructed composed of the selection of a pair of the informational tools mentioned above, in which the different dynamical regimes appeared very clear and give more information of the underlying process.
...

References

SHOWING 1-9 OF 9 REFERENCES

Analysis of Observed Chaotic Data

Regular Dynamics: Newton to Poincare KAM Theorem, and the Chaos Toolkit: Making 'Physics' out of Chaos.

Iterated maps on the interval as dynamical systems

Motivation and Interpretation.- One-Parameter Families of Maps.- Typical Behavior for One Map.- Parameter Dependence.- Systematics of the Stable Periods.- On the Relative Frequency of Periodic and

What is ergodic theory

Ergodic theory involves the study of transformations on measure spaces. Interchanging the words “measurable function” and “probability density function” translates many results from real analysis to

DIMENSION THEORY IN DYNAMICAL SYSTEMS: CONTEMPORARY VIEWS AND APPLICATIONS By YAKOV B. PESIN Chicago Lectures in Mathematics, University of Chicago Press, 312 pp. Price: hardback $56, paperback $19.95. ISBN 0 226 66222 5

  • Y. Pesin
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1998
Books, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with, become what you need to get.

Digital processing of speech signals

  • M. Bellanger
  • Computer Science, Mathematics
    Proceedings of the IEEE
  • 1980

Dimension theory in dynamical systems

Trans

  • Moscow Math. Soc. 2, 127
  • 1983

Discr

  • Cont. Dyn. Systems 7, 477
  • 2001

submitted to Phys

  • Rep.
  • 2000