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Entropy Measures to Assess Irregularity and Complexity of Time Series and Multidimensional Data

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

Deadline for manuscript submissions: closed (21 June 2024) | Viewed by 2984

Special Issue Editors


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Guest Editor
School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh EH9 3FB, UK
Interests: connectivity; biomedical signal processing; nonlinear analysis; brain activity; multiway array analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Entropy-based metrics issued from information theory have found an increasing interest in the dynamical analysis of different kinds of systems. Extensions of these nonlinear measures to multidimensional and/or multivariate data have also led to the publication of many papers from several areas. Moreover, analyses of entropy measures over several temporal or spatial scales are now commonly used to quantify the complexity of systems.

In this Special Issue, we would like to collect papers focusing on the recent advances and challenges of entropy measures (including applications to graphs and multidimensional entropy measures). Papers presenting theoretical backgrounds of entropy measures are also welcome, together with applications of the most recent algorithms to quantify the irregularity and complexity of time series, images and other forms of recordings. Papers presenting theoretical aspects or applications on multivariate data are also in the scope of this Special Issue.

Dr. Anne Humeau-Heurtier
Dr. Javier Escudero
Guest Editors

Manuscript Submission Information

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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

  • irregularity
  • complexity
  • entropy
  • time series
  • multidimensional data
  • graphs
  • multivariate data

Published Papers (2 papers)

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Research

16 pages, 1404 KiB  
Article
Criticality Analysis: Bio-Inspired Nonlinear Data Representation
by Tjeerd V. olde Scheper
Entropy 2023, 25(12), 1660; https://doi.org/10.3390/e25121660 - 14 Dec 2023
Cited by 1 | Viewed by 1225
Abstract
The representation of arbitrary data in a biological system is one of the most elusive elements of biological information processing. The often logarithmic nature of information in amplitude and frequency presented to biosystems prevents simple encapsulation of the information contained in the input. [...] Read more.
The representation of arbitrary data in a biological system is one of the most elusive elements of biological information processing. The often logarithmic nature of information in amplitude and frequency presented to biosystems prevents simple encapsulation of the information contained in the input. Criticality Analysis (CA) is a bio-inspired method of information representation within a controlled Self-Organised Critical system that allows scale-free representation. This is based on the concept of a reservoir of dynamic behaviour in which self-similar data will create dynamic nonlinear representations. This unique projection of data preserves the similarity of data within a multidimensional neighbourhood. The input can be reduced dimensionally to a projection output that retains the features of the overall data, yet has a much simpler dynamic response. The method depends only on the Rate Control of Chaos applied to the underlying controlled models, which allows the encoding of arbitrary data and promises optimal encoding of data given biologically relevant networks of oscillators. The CA method allows for a biologically relevant encoding mechanism of arbitrary input to biosystems, creating a suitable model for information processing in varying complexity of organisms and scale-free data representation for machine learning. Full article
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22 pages, 8766 KiB  
Article
Research on the Threshold Determination Method of the Duffing Chaotic System Based on Improved Permutation Entropy and Poincaré Mapping
by Jing Zhou, Yaan Li and Mingzhou Wang
Entropy 2023, 25(12), 1654; https://doi.org/10.3390/e25121654 - 13 Dec 2023
Cited by 1 | Viewed by 1069
Abstract
The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Traditional methods such as Melnikov theory, the Poincaré [...] Read more.
The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Traditional methods such as Melnikov theory, the Poincaré section quantitative discrimination method, and experimental analyses based on phase diagram segmentation have limitations in accuracy and efficiency. In addition, they require large computational data and complex algorithms while having slow convergence. Improved permutation entropy incorporates signal amplitude information on the basis of permutation entropy and has better noise resistance. According to the characteristics of improved permutation entropy, a threshold determination method for the Duffing chaotic oscillator detection system based on improved permutation entropy (IPE) and Poincaré mapping (PM) is proposed. This new metric is called Poincaré mapping improved permutation entropy (PMIPE). The simulation results and the verification results of real underwater acoustic signals indicate that our proposed method outperforms traditional methods in terms of accuracy, simplicity, and stability. Full article
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