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Entropy
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Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis
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Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (22 December 2021) | Viewed by 13215

Special Issue Editors

Dr. Miguel C. Soriano

E-Mail Website
Guest Editor
Institute for Cross-Disciplinary Physics and Complex Systems, IFISC (CSIC-UIB), Palma, Spain
Interests: complex systems; permutation entropy; reservoir computing; nonlinear dynamical systems; time series analysis; information processing
Dr. Luciano Zunino

E-Mail Website
Guest Editor
Centro de Investigaciones Ópticas (CONICET La Plata—CIC—UNLP), La Plata, Buenos Aires, Argentina
Interests: time series analysis; nonlinear dynamics; complex systems; data analysis; permutation entropy; ordinal patterns; chaos; long-range correlations; fractality; multifractality
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

When observing the world, we are often confronted with the need to analyze time series of unknown origin. We look for tools and techniques that are free of restrictive parametric model assumptions and can account for the temporal ordering structure in the time series. The main objective is to try to shed some lights on the underlying mechanisms that govern the system’s dynamics. This information can then be used to model and predict the behavior of the system under study. Methods that rely on the notions of entropy and ordinal symbolic dynamics offer a competitive edge since they are robust with respect to noise, computationally efficient, flexible, and invariant with respect to nonlinear monotonic transformations of the data. They have been shown to be especially useful for characterization, discrimination and classification purposes. Furthermore, a large amount of data with outliers and artifacts can be quickly, automatically and successfully analyzed by using these ordinal tools. Examples of methods based on constructing an ordinal symbolic representation of the time series that can unveil the complex dynamical content of nonlinear time series are the multiscale permutation entropy and its variants, the ordinal autocorrelation functions, the decay of the number of forbidden/unobserved ordinal patterns as a function of the time series length, and the quantifiers derived from ordinal transition networks, to mention only a few.

This Special Issue aims at identifying ordinal and pattern-based quantifiers for complex time series analysis. Applications of interest include, but are not limited to, the analysis of nonlinear systems with multiple timescales, the discrimination of different types of temporal correlations, the distinction between chaotic and stochastic dynamics, the identification of temporal scales characteristic of the underlying temporal dynamics, time series classification, time series segmentation, and time series irreversibility.

Dr. Miguel C. Soriano
Dr. Luciano Zunino
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • ordinal patterns
  • permutation entropy
  • ordinal autocorrelation functions
  • forbidden ordinal patterns
  • unobserved ordinal patterns
  • ordinal transition networks
  • time series analysis
  • nonlinear dynamical systems
  • delayed feedback
  • complex systems

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Published Papers (5 papers)

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Research

10 pages, 344 KiB  
Article
Permutation Entropy of Weakly Noise-Affected Signals
by Leonardo Ricci and Antonio Politi
Entropy 2022, 24(1), 54; https://doi.org/10.3390/e24010054 - 28 Dec 2021
Cited by 4 | Viewed by 2012
Abstract
We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed [...] Read more.
We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations. Full article
(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)
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16 pages, 324 KiB  
Article
On Rényi Permutation Entropy
by Tim Gutjahr and Karsten Keller
Entropy 2022, 24(1), 37; https://doi.org/10.3390/e24010037 - 24 Dec 2021
Cited by 4 | Viewed by 2397
Abstract
Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies [...] Read more.
Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for q=1. Its relationship to Kolmogorov–Sinai entropy and, for q=2, to the recently introduced symbolic correlation integral are touched. Full article
(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)
14 pages, 1295 KiB  
Article
Evaluating Temporal Correlations in Time Series Using Permutation Entropy, Ordinal Probabilities and Machine Learning
by Bruno R. R. Boaretto, Roberto C. Budzinski, Kalel L. Rossi, Thiago L. Prado, Sergio R. Lopes and Cristina Masoller
Entropy 2021, 23(8), 1025; https://doi.org/10.3390/e23081025 - 9 Aug 2021
Cited by 6 | Viewed by 2850
Abstract
Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on [...] Read more.
Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on training a machine learning algorithm to predict the temporal correlation parameter, α, of flicker noise (FN) time series. The algorithm is trained using as input features the probabilities of ordinal patterns computed from FN time series, xαFN(t), generated with different values of α. Then, the ordinal probabilities computed from the time series of interest, x(t), are used as input features to the trained algorithm and that returns a value, αe, that contains meaningful information about the temporal correlations present in x(t). We have also shown that the difference, Ω, of the permutation entropy (PE) of the time series of interest, x(t), and the PE of a FN time series generated with α=αe, xαeFN(t), allows the identification of the underlying determinism in x(t). Here, we apply our methodology to different datasets and analyze how αe and Ω correlate with well-known quantifiers of chaos and complexity. We also discuss the limitations for identifying determinism in highly chaotic time series and in periodic time series contaminated by noise. The open source algorithm is available on Github. Full article
(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)
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15 pages, 971 KiB  
Article
Time-Delay Identification Using Multiscale Ordinal Quantifiers
by Miguel C. Soriano and Luciano Zunino
Entropy 2021, 23(8), 969; https://doi.org/10.3390/e23080969 - 27 Jul 2021
Cited by 6 | Viewed by 2274
Abstract
Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. [...] Read more.
Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon. Full article
(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)
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11 pages, 4403 KiB  
Article
Chaotic Time-Delay Signature Suppression and Entropy Growth Enhancement Using Frequency-Band Extractor
by Yanqiang Guo, Tong Liu, Tong Zhao, Haojie Zhang and Xiaomin Guo
Entropy 2021, 23(5), 516; https://doi.org/10.3390/e23050516 - 23 Apr 2021
Cited by 6 | Viewed by 2157
Abstract
By frequency-band extracting, we experimentally and theoretically investigate time-delay signature (TDS) suppression and entropy growth enhancement of a chaotic optical-feedback semiconductor laser under different injection currents and feedback strengths. The TDS and entropy growth are quantified by the peak value of autocorrelation function [...] Read more.
By frequency-band extracting, we experimentally and theoretically investigate time-delay signature (TDS) suppression and entropy growth enhancement of a chaotic optical-feedback semiconductor laser under different injection currents and feedback strengths. The TDS and entropy growth are quantified by the peak value of autocorrelation function and the difference of permutation entropy at the feedback delay time. At the optimal extracting bandwidth, the measured TDS is suppressed up to 96% compared to the original chaos, and the entropy growth is higher than the noise-dominated threshold, indicating that the dynamical process is noisy. The effects of extracting bandwidth and radio frequencies on the TDS and entropy growth are also clarified experimentally and theoretically. The experimental results are in good agreements with the theoretical results. The skewness of the laser intensity distribution is effectively improved to 0.001 with the optimal extracting bandwidth. This technique provides a promising tool to extract randomness and prepare desired entropy sources for chaotic secure communication and random number generation. Full article
(This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis)
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