Topological properties of the limited penetrable horizontal visibility graph family

Wang, Minggang; Vilela, André L. M.; Du, Ruxu; Zhao, Longfeng; Dong, Gaogao; Li, Tian; Stanley, H. Eugene

doi:10.1103/physreve.97.052117

Cited by 13 publications

(3 citation statements)

References 54 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

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“…The directed-limited penetrable horizontal visibility graph (DLPHVG) and the image-limited penetrable horizontal visibility graph (ILPHVG), which are named as the LPHVG family, have also been developed [ 93 ]. Numerical experiments have been taken to investigate topological properties of these networks, and they can be used to show the irreversibility of time series and discriminate noise from chaos.…”

Section: Visibility Graphmentioning

confidence: 99%

Visibility graph for time series prediction and image classification: a review

2022

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The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

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“…Its advantage is that the associated network not only inherits the inherent characteristics of the original time series, but also is convenient to analyze the dynamic characteristics of the time series. Therefore, visibility graph, horizontal visibility graph, penetrable visibility graph, directed limited penetrable visibility graph have gradually become important branches in the study of time series [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Research on the Interdependent Network of the Thermal Coal Price Based on Directed Limited Penetrable Visibility Graph

Zhang,

Tian,

et al. 2021

Preprint

Self Cite

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This paper constructs a new directed limited penetrable interdependent network (DLPIN) for the thermal coal price (TCP) between the opening series and closing series based on the criterion of the visibility graph, which is better than the traditional method of the visibility graph to mine the price information for steam coal. According to the DLPIN by analyzing, the mechanism of the price fluctuation and information transmission for the thermal coal can be obtained, some references can be provided for the investors to reduce risk investment and increase revenue.

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Topological properties of the limited penetrable horizontal visibility graph family

Cited by 13 publications

References 54 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

Visibility graph for time series prediction and image classification: a review

Research on the Interdependent Network of the Thermal Coal Price Based on Directed Limited Penetrable Visibility Graph

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