Permutation entropy revisited

Stuart J. Watt, Antonio Politi (Corresponding Author)

Research output: Contribution to journalArticle

1 Citation (Scopus)
2 Downloads (Pure)

Abstract

Time-series analysis in terms of ordinal patterns is revisited by introducing a generalized permutation entropy Hp(w, L), which depends on two different window lengths: w, implicitly defining the resolution of the underlying partition; L, playing the role of an embedding dimension, analogously to standard nonlinear time-series analysis. The w-dependence provides information on the structure of the corresponding invariant measure, while the L-dependence helps determining the Kolmogorov–Sinai entropy. We finally investigate the structure of the partition with the help of principal component analysis, finding that, upon increasing w, the single atoms become increasingly elongated.
Original languageEnglish
Pages (from-to)95-99
Number of pages5
JournalChaos, Solitons & Fractals
Volume120
Early online date31 Jan 2019
DOIs
Publication statusPublished - 1 Mar 2019

Fingerprint

Permutation
Entropy
Partition
Nonlinear Time Series Analysis
Time Series Analysis
Invariant Measure
Principal Component Analysis
Standards

Keywords

  • fractal dimension
  • time series
  • entropy
  • embedding
  • complexity
  • PCA

Cite this

Permutation entropy revisited. / Watt, Stuart J.; Politi, Antonio (Corresponding Author).

In: Chaos, Solitons & Fractals, Vol. 120, 01.03.2019, p. 95-99.

Research output: Contribution to journalArticle

Watt, Stuart J. ; Politi, Antonio. / Permutation entropy revisited. In: Chaos, Solitons & Fractals. 2019 ; Vol. 120. pp. 95-99.
@article{4f7714b622f843549500daba885c37df,
title = "Permutation entropy revisited",
abstract = "Time-series analysis in terms of ordinal patterns is revisited by introducing a generalized permutation entropy Hp(w, L), which depends on two different window lengths: w, implicitly defining the resolution of the underlying partition; L, playing the role of an embedding dimension, analogously to standard nonlinear time-series analysis. The w-dependence provides information on the structure of the corresponding invariant measure, while the L-dependence helps determining the Kolmogorov–Sinai entropy. We finally investigate the structure of the partition with the help of principal component analysis, finding that, upon increasing w, the single atoms become increasingly elongated.",
keywords = "fractal dimension, time series, entropy, embedding, complexity, PCA",
author = "Watt, {Stuart J.} and Antonio Politi",
note = "Acknowledgment One of us, (SJW), wishes to acknowledge financial support from the Carnegie Trust for his summer project.",
year = "2019",
month = "3",
day = "1",
doi = "10.1016/j.chaos.2018.12.039",
language = "English",
volume = "120",
pages = "95--99",
journal = "Chaos, Solitons & Fractals",
issn = "0960-0779",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Permutation entropy revisited

AU - Watt, Stuart J.

AU - Politi, Antonio

N1 - Acknowledgment One of us, (SJW), wishes to acknowledge financial support from the Carnegie Trust for his summer project.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - Time-series analysis in terms of ordinal patterns is revisited by introducing a generalized permutation entropy Hp(w, L), which depends on two different window lengths: w, implicitly defining the resolution of the underlying partition; L, playing the role of an embedding dimension, analogously to standard nonlinear time-series analysis. The w-dependence provides information on the structure of the corresponding invariant measure, while the L-dependence helps determining the Kolmogorov–Sinai entropy. We finally investigate the structure of the partition with the help of principal component analysis, finding that, upon increasing w, the single atoms become increasingly elongated.

AB - Time-series analysis in terms of ordinal patterns is revisited by introducing a generalized permutation entropy Hp(w, L), which depends on two different window lengths: w, implicitly defining the resolution of the underlying partition; L, playing the role of an embedding dimension, analogously to standard nonlinear time-series analysis. The w-dependence provides information on the structure of the corresponding invariant measure, while the L-dependence helps determining the Kolmogorov–Sinai entropy. We finally investigate the structure of the partition with the help of principal component analysis, finding that, upon increasing w, the single atoms become increasingly elongated.

KW - fractal dimension

KW - time series

KW - entropy

KW - embedding

KW - complexity

KW - PCA

U2 - 10.1016/j.chaos.2018.12.039

DO - 10.1016/j.chaos.2018.12.039

M3 - Article

VL - 120

SP - 95

EP - 99

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

ER -