Degree distributions and motif profiles of Thue–Morse complex network

Hu, Xiaohua; Niu, Min

doi:10.1016/j.chaos.2023.114141

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…The LPHVG is an enhancement of the HVG. By setting the limited penetrable distance to ρ, a link between two nodes exists if the number of in-between nodes that block the horizontal line is at most ρ [43][44][45][46][47]. If ρ = 0, LPHVG degenerates into HVG, but if ρ ̸ = 0, there are more connections between any two nodes in LPHVG than in HVG.…”

Section: Limited Penetrable Horizontal Visibility Graphmentioning

confidence: 99%

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

Angelidis,

Goulas,

Bratsas

et al. 2024

Entropy

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We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.

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Section: Limited Penetrable Horizontal Visibility Graphmentioning

confidence: 99%

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

Angelidis,

Goulas,

Bratsas

et al. 2024

Entropy

View full text Add to dashboard Cite

show abstract

“…Li and Shang introduced a combination of the amplitude difference distribution with discrete generalized past entropy to present a new method called discrete generalized past entropy based on the amplitude difference distribution of the horizontal visibility graph (AHVG-DGPE). The authors note its efficiency in systems evaluation and its higher accuracy and sensitivity rate than the traditional method in characterizing dynamic systems; see [40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

Conejero,

Velichko,

Garibo-i-Orts

et al. 2024

Mathematics

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The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Interfacing. As several entropy measures exist, the problem is assessing the effectiveness of entropies used as features for the ML classification of nonlinear dynamics of time series. We propose a method, called global efficiency (GEFMCC), for assessing the effectiveness of entropy features using several chaotic mappings. GEFMCC is a fitness function for optimizing the type and parameters of entropies for time series classification problems. We analyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) for four discrete mappings, the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn has greater GEFMCC in the classification task compared to NNetEn. However, NNetEn classification efficiency is higher than FuzzyEn for some local areas of the time series dynamics. The results of using horizontal visibility graphs (HVG) instead of the raw time series demonstrate the GEFMCC decrease after HVG time series transformation. However, the GEFMCC increases after applying the HVG for some local areas of time series dynamics. The scientific community can use the results to explore the efficiency of the entropy-based classification of time series in “The Entropy Universe”. An implementation of the algorithms in Python is presented.

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“…Li and Shang introduce a combination of the amplitude difference distribution with discrete generalized past entropy to present a new method called Discrete Generalized Past Entropy based on the Amplitude Difference Distribution of the Horizontal Visibility Graph (AHVG-DGPE). The authors note its efficiency in systems evaluation and higher accuracy and sensitivity rate compared to the traditional method in characterizing dynamic systems, see also [24][25][26] In this paper, we propose a method for assessing the effectiveness of entropies using chaotic mappings: We use it for analyzing the FuzzyEn and NNetEn entropies on four discrete mappings is given: the logistic map, the sine map, the Planck map, and the two-memristor based map. We use the corresponding HVG degrees representation of these time series, which implies that the resulting time series does not consist of real numbers but only of integer numbers.…”

Section: Introductionmentioning

confidence: 99%

Exploring Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

Conejero,

Velichko,

Garibo-i-Orts

et al. 2023

Preprint

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In this paper, we propose a method for assessing the effectiveness of entropy features using several chaotic mappings. We anlyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) on four discrete mappings: the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn is shown to have improved global efficiency (GEFMCC) in the classification task compared to NNetEn. At the same time, there are local areas of the time series dynamics in which the classification efficiency NNetEn is higher than FuzzyEn. The results of using horizontal visibility graphs (HVG) instead of the raw time series are also shown. GEFMCC decreases after HVG time series transformation, but there are local areas of the time series dynamics in which the classification efficiency increases after including the HVG. The scientific community can use the results to explore the efficiency of entropy-based classification of time series.

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Degree distributions and motif profiles of Thue–Morse complex network

Cited by 4 publications

References 29 publications

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs

Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

Exploring Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

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