A novel visibility graph transformation of time series into weighted networks

Recent observation studies have revealed that earthquakes are classified into several different categories. Each category might be characterized by the unique statistical feature in the time series, but the present understanding is still limited due to their non-linear and non-stationary nature. Here we utilize complex network theory to shed new light on the statistical properties of earthquake time series. We investigate two kinds of time series, which are magnitude and inter-event time (IET), for three different categories of earthquakes: regular earthquakes, earthquake swarms, and tectonic tremors. Following the criterion of visibility graph, earthquake time series are mapped into a complex network by considering each seismic event as a node and determining the links. As opposed to the current common belief, it is found that the magnitude time series are not statistically equivalent to random time series. The IET series exhibit correlations similar to fractional Brownian motion for all the categories of earthquakes. Furthermore, we show that the time series of three different categories of earthquakes can be distinguished by the topology of the associated visibility graph. Analysis on the assortativity coefficient also reveals that the swarms are more intermittent than the tremors.

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Visibility Graph Power Geometric Aggregation Operator and Its Application in Water, Energy and Food Efficiency Evaluation

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph17113891 ◽

2020 ◽

Vol 17 (11) ◽

pp. 3891

Author(s):

Lihua Liu ◽

Jing Huang ◽

Huimin Wang

Keyword(s):

Time Series ◽

Time Series Data ◽

Coupling Efficiency ◽

Aggregation Operator ◽

Visibility Graph ◽

Series Data ◽

Efficiency Evaluation ◽

Geometric Operator ◽

The Relationship

In the real decision-making process, there are so many time series values that need to be aggregated. In this paper, a visibility graph power geometric (VGPG) aggregation operator is developed, which is based on the complex network and power geometric operator. Time series data are converted into a visibility graph. A visibility matrix is developed to denote the links among different time series values. A new support function based on the distance of two values are proposed to measure the support degree of each other when the two time series values have visibility. The VGPG operator considers not only the relationship but also the similarity degree between two values. Meanwhile, some properties of the VGPG operator are also investigated. Finally, a case study for water, energy, and food coupling efficiency evaluation in China is illustrated to show the effectiveness of the proposed operator. Comparative analysis with the existing research is also offered to show the advantages of the proposed method.

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Analyses on Volatility Clustering in Financial Time-Series Using Clustering Indices, Asymmetry, and Visibility Graph

IEEE Access ◽

10.1109/access.2020.3037240 ◽

2020 ◽

Vol 8 ◽

pp. 208779-208795

Author(s):

Kyungwon Kim ◽

Jae Wook Song

Keyword(s):

Time Series ◽

Financial Time Series ◽

Visibility Graph ◽

Volatility Clustering ◽

Financial Time

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Analysing the Dynamics of Interbeat Interval Time Series Using Grouped Horizontal Visibility Graph

IEEE Access ◽

10.1109/access.2018.2890542 ◽

2019 ◽

Vol 7 ◽

pp. 9926-9934 ◽

Cited By ~ 3

Author(s):

Gulraiz Iqbal Choudhary ◽

Wajid Aziz ◽

Ishtiaq Rasool Khan ◽

Susanto Rahardja ◽

Pasi Franti

Keyword(s):

Time Series ◽

Visibility Graph ◽

Interbeat Interval ◽

Horizontal Visibility ◽

Interval Time ◽

Interval Time Series ◽

Horizontal Visibility Graph

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Surface Electromyography-Based Muscle Fatigue Analysis Using Binary and Weighted Visibility Graph Features

Fluctuation and Noise Letters ◽

10.1142/s0219477521500164 ◽

2020 ◽

pp. 2150016

Author(s):

Navaneethakrishna Makaram ◽

P. A. Karthick ◽

Venugopal Gopinath ◽

Ramakrishnan Swaminathan

Keyword(s):

Muscle Fatigue ◽

Surface Electromyography ◽

Sports Medicine ◽

Biceps Brachii ◽

Information Gain ◽

Graph Transformation ◽

Visibility Graph ◽

Invasive Technique ◽

Learning Machines ◽

Significant Difference

Surface electromyography (sEMG) is a non-invasive technique to assess the electrical activity of contracting skeletal muscles. sEMG-based muscle fatigue detection plays a key role in sports medicine, ergonomics and rehabilitation. These signals are random, multicomponent, nonlinear and the degree of fluctuations is higher in dynamic contractions. Hence, the extraction of reliable biomarkers remains a challenging task. In this work, an attempt has been made to differentiate non-fatigue, and fatigue conditions using nonlinear techniques, namely, binary and weighted Visibility Graph (VG) features. For this, signals are recorded from the biceps brachii muscle of 52 healthy adult volunteers. These signals are preprocessed, and the contractions associated with the non-fatigue and fatigue conditions are segmented. The graph transformation is performed, and first-order and second-order statistics, along with entropy measures, are extracted from the degree distribution. Parametric and non-parametric machine learning methods are applied for the classification. The results show that the proposed VG approach is able to capture the fluctuations of the signals in non-fatigue and fatigue conditions. Further, all extracted features exhibit a significant difference with [Formula: see text] [Formula: see text]. Maximum accuracy of 89.1% is achieved with information gain selected features and extreme learning machines classifier. Additionally, weighted VG features perform better than the binary version with a difference in the accuracy of 5%. It appears that the proposed approach could be used in real-time implementation for the monitoring of muscle fatigue conditions.

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Examination of Chaotic Structures in Semiconductor or Alloy Voltage Time-Series: A Complex Network Approach for the Case of TlInTe2

Physics ◽

10.3390/physics2040036 ◽

2020 ◽

Vol 2 (4) ◽

pp. 624-639

Author(s):

Dimitrios Tsiotas ◽

Lykourgos Magafas ◽

Michael P. Hanias

Keyword(s):

Time Series ◽

Network Analysis ◽

Complex Network ◽

Graph Algorithm ◽

Differential Resistance ◽

Visibility Graph ◽

Characteristic Region ◽

Scale Free ◽

Complex Network Analysis ◽

Voltage Oscillation

This paper proposes a method for examining chaotic structures in semiconductor or alloy voltage oscillation time-series, and focuses on the case of the TlInTe2 semiconductor. The available voltage time-series are characterized by instabilities in negative differential resistance in the current–voltage characteristic region, and are primarily chaotic in nature. The analysis uses a complex network analysis of the time-series and applies the visibility graph algorithm to transform the available time-series into a graph so that the topological properties of the graph can be studied instead of the source time-series. The results reveal a hybrid lattice-like configuration and a major hierarchical structure corresponding to scale-free characteristics in the topology of the visibility graph, which is in accordance with the default hybrid chaotic and semi-periodic structure of the time-series. A novel conceptualization of community detection based on modularity optimization is applied to the available time-series and reveals two major communities that are able to be related to the pair-wise attractor of the voltage oscillations’ phase portrait of the TlInTe2 time-series. Additionally, the network analysis reveals which network measures are more able to preserve the chaotic properties of the source time-series. This analysis reveals metric information that is able to supplement the qualitative phase-space information. Overall, this paper proposes a complex network analysis of the time-series as a method for dealing with the complexity of semiconductor and alloy physics.

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