Visibility Graph Method Research Articles

Feature analysis of 5G traffic data based on visibility graph

IntroductionAs 5G networks become widespread and their application scenarios expand, massive amounts of traffic data are continuously generated. Properly analyzing this data is crucial for enhancing 5G services.MethodsThis paper uses the visibility graph method to convert 5G traffic data into a visibility graph network, conducting a feature analysis of the 5G traffic data. Using the AfreecaTV dataset as the research object, this paper constructs visibility networks at different scales and observes the evolution of degree distribution with varying data volumes. The paper employs the Hurst index to evaluate the 5G traffic network and uses community detection to study the networks converted from 5G traffic data of different applications.ResultsExperimental results reveal significant differences in node degree distribution and topological structures of 5G traffic data across different application scenarios, such as star structures and multiple subnetwork structures. It is found that the node degree distribution of 5G traffic networks exhibits heterogeneity, reflecting the uneven growth of node degrees during network expansion. The Hurst index analysis discovers that the 5G traffic network retains the long-term dependence and trends of the original data. Through community detection, it is observed that networks converted from 5G traffic data of different applications exhibit diverse community structures, such as high centrality nodes, star-like community structures, modularity, and multilayer characteristics.DiscussionThese findings indicate that 5G traffic networks in different application scenarios exhibit complex and diverse characteristics. The heterogeneity of node degree distribution and differences in topological structures reflect the imbalance in node connection methods during network expansion. The results of the Hurst index show that the 5G traffic network inherits the long-term dependence of the original data, providing a basis for analyzing the dynamic characteristics of the network. The diverse community structures reveal the inherent modularity and hierarchy of the network, which helps to understand the performance and optimization directions of 5G networks in different applications.

Information–Theoretic Analysis of Visibility Graph Properties of Extremes in Time Series Generated by a Nonlinear Langevin Equation

In this study, we examined how the nonlinearity α of the Langevin equation influences the behavior of extremes in a generated time series. The extremes, defined according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the influence of the nonlinearity α on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main finding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly influenced by the nonlinearity, which decreases with with an increase in α. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity.

Analysis of differences in fossil fuel consumption in the world based on the fractal time series and complex network

Fossil fuels remain indispensable energy resources despite their non-renewable nature. Understanding the patterns of global fossil fuel consumption is essential for energy security and policy-making. This study employs complex network theory and fractal time series analysis to explore the underlying dynamics and patterns of fossil fuel consumption globally, with a focus on coal, oil, and gas consumption.The study applies the Hurst index to raw fossil fuel consumption data to identify fractal characteristics. Additionally, the visibility graph method is used to convert time series data into complex networks, allowing further analysis of consumption patterns. The study examines fossil fuel consumption in 38 countries to assess global trends and differences. The analysis reveals that global fossil fuel consumption follows a fractal time series pattern, with Hurst index values exceeding 0.9, indicating long-term memory characteristics. The application of the visibility graph method demonstrates variations in the Hurst index of degree distribution, enabling the differentiation of consumption patterns across regions. The method also uncovers distinct features of coal, oil, and gas consumption when viewed from a network perspective. The findings suggest that fossil fuel consumption has predictable long-term patterns, which are crucial for assessing future energy demands. The study highlights the importance of legislative measures to safeguard fossil fuel resources, especially for countries like China, where energy security and international competitiveness are paramount. Understanding these consumption patterns could guide future energy policies aimed at managing non-renewable resources more effectively.

Statistical Exploration of the Salar de Atacama’s: Brine Measurements of the Basin Wells

Abstract In this study, we conduct a statistical analysis using the 4-plot, visibility graph, and horizontal visibility graph methods on brine extraction data from the Salar de Atacama basin in Chile. The 4-plot reveals real trends in the data that could lead model proposals. Conversely, complex networks analysis yields no significant findings, suggesting that the data lacks internal structural features and appears random. This randomness underscores the decision-making processes and highlights areas for potential optimization.

A two‐phase features extraction approach for BRB based fault diagnosis of electromechanical system

SummaryBelief rule base (BRB) is an effective nonlinear relationship modeling approach. It has been widely used in the fault diagnosis of electromechanical systems. To improve the performance of the BRB‐based diagnostic model, a two‐phase features extraction approach called CNPCA based on complex network (CN) and principal component analysis (PCA) is proposed in this paper. In the first phase, the weighted visibility graph method is applied to transform the time series data of monitored variables into complex networks. Then the statistical attributes of the constructed networks are extracted as the initial features. In the second phase, the PCA method is used to process the initial features and the principal component features are obtained. After that, the CNPCA‐BRB diagnostic model for the electromechanical system is constructed. The experimental results of the elevator fault diagnosis show that the constructed diagnostic model outperforms better than the classical ones. It demonstrates that the CNPCA approach can ensure the integrity of fault information in the features and improve the separability of the fault features.

Rapeseed Seed Coat Color Classification Based on the Visibility Graph Algorithm and Hyperspectral Technique

Information technology and statistical modeling have made significant contributions to smart agriculture. Machine vision and hyperspectral technologies, with their non-destructive and real-time capabilities, have been extensively utilized in the non-destructive diagnosis and quality monitoring of crops and seeds, becoming essential tools in traditional agriculture. This work applies these techniques to address the color classification of rapeseed, which is of great significance in the field of rapeseed growth diagnosis research. To bridge the gap between machine vision and hyperspectral technology, a framework is developed that includes seed color calibration, spectral feature extraction and fusion, and the recognition modeling of three seed colors using four machine learning methods. Three categories of rapeseed coat colors are calibrated based on visual perception and vector-square distance methods. A fast-weighted visibility graph method is employed to map the spectral reflectance sequences to complex networks, and five global network attributes are extracted to fuse the full-band reflectance as model input. The experimental results demonstrate that the classification recognition rate of the fused feature reaches 0.943 under the XGBoost model, confirming the effectiveness of the network features as a complement to the spectral reflectance. The high recognition accuracy and simple operation process of the framework support the further application of hyperspectral technology to analyze the quality of rapeseed.

Exploring EEG Emotion Recognition through Complex Networks: Insights from the Visibility Graph of Ordinal Patterns

The construction of complex networks from electroencephalography (EEG) proves to be an effective method for representing emotion patterns in affection computing as it offers rich spatiotemporal EEG features associated with brain emotions. In this paper, we propose a novel method for constructing complex networks from EEG signals for emotion recognition, which begins with phase space reconstruction to obtain ordinal patterns and subsequently forms a graph network representation from the sequence of ordinal patterns based on the visibility graph method, named ComNet-PSR-VG. For the proposed ComNet-PSR-VG, the initial step involves mapping EEG signals into a series of ordinal partitions using phase space reconstruction, generating a sequence of ordinal patterns. These ordinal patterns are then quantified to form a symbolized new sequence. Subsequently, the resulting symbolized sequence of ordinal patterns is transformed into a graph network using the visibility graph method. Two types of network node measures, average node degree (AND) and node degree entropy (NDE), are extracted from the graph networks as the inputs of machine learning for EEG emotion recognition. To evaluate the effectiveness of the proposed construction method of complex networks based on the visibility graph of ordinal patterns, comparative experiments are conducted using two types of simulated signals (random and Lorenz signals). Subsequently, EEG emotion recognition is performed on the SEED EEG emotion dataset. The experimental results show that, with AND as the feature, our proposed method is 4.88% higher than the existing visibility graph method and 12.23% higher than the phase space reconstruction method. These findings indicate that our proposed novel method for constructing complex networks from EEG signals not only achieves effective emotional EEG pattern recognition but also exhibits the potential for extension to other EEG pattern learning tasks, suggesting broad adaptability and application potential for our method.

Bursting-process modulation in a turbulent boundary layer via the natural visibility graph method

This study proposes a new method for detecting bursting events based on a natural visibility graph and reveals the amplitude modulation of the large-scale to small-scale bursting processes. Through hot-wire measurements of the turbulent boundary layer, velocity signal sequences with different normal heights are obtained. First, a natural visibility graph method is used to map the velocity signal into a visibility network to obtain a time series of the network degree centrality. Next, a statistical analysis of the degree centrality shows that it can reflect hidden structural characteristics. Moreover, the degree centrality signals have a comparable spatial/temporal scale to the Taylor microscale, which indicates that the degree centrality could provide a potential method to characterize the instantaneous wavenumber/frequency information of small-scales. Then, a new method for detecting bursting events is provided based on the degree centrality values. Characterizations of small-scale bursting events are investigated, providing results for the amplitude modulation between large-scale and small-scale bursting processes. These results show that, in the near-wall region, an increase in amplitudes of a small-scale bursting process is induced for intervals of positive large-scale fluctuations and vice versa for negative large-scale fluctuations. The outer zone shows opposite. The phenomenon of temporal shifting of the amplitude modulation is then investigated and shows that the high-speed large-scales lag behind the small-scale bursting process in the near-wall region, while the outer region shows the opposite. The distance of the small-scale bursting processes leading to the large-scales in the near-wall space is log-linear with the wall-normal height.

Investigation of the Global Stock Trading Based on Visibility Graph and Entropy Weight Method

The increasing complexity and dynamics of the stock trading market are major challenges for the financial industry and are primary dilemmas for all countries nowadays. In addition, the stock trading market has a considerable impact on the global economy, and its importance is self-evident. To cope with the complexity and dynamics of a stock trading market, this paper applies complex network theory and model to explore the topology of the global stock trading network. First, this paper collects stock trading data from 74 countries from 1999 to 2020. It converts the collected stock trading data of these countries into a complex network using a type of algorithm based on the time series visibility graph (VG) algorithm. Then, the data are analyzed by a complex network model, and six analytical metrics are obtained. Finally, the six metrics are analyzed by the entropy weight method to identify the key nodes in the network and to obtain the ranking of each country’s stock trading data. This paper is an effective application of complex network and entropy weight method in stock trend analysis, which mainly includes two contributions. First, the VG algorithm provides a novel research perspective for modeling the global stock trading trend. Second, key nodes in the network are analyzed and identified based on the entropy weight method, and the ranking of key nodes in the stock trading network is obtained, which provides a new method for further research on the stock trading trend, investment portfolio, and stock return forecasting.

Automatic snoring detection using a hybrid 1D–2D convolutional neural network

Snoring, as a prevalent symptom, seriously interferes with life quality of patients with sleep disordered breathing only (simple snorers), patients with obstructive sleep apnea (OSA) and their bed partners. Researches have shown that snoring could be used for screening and diagnosis of OSA. Therefore, accurate detection of snoring sounds from sleep respiratory audio at night has been one of the most important parts. Considered that the snoring is somewhat dangerously overlooked around the world, an automatic and high-precision snoring detection algorithm is required. In this work, we designed a non-contact data acquire equipment to record nocturnal sleep respiratory audio of subjects in their private bedrooms, and proposed a hybrid convolutional neural network (CNN) model for the automatic snore detection. This model consists of a one-dimensional (1D) CNN processing the original signal and a two-dimensional (2D) CNN representing images mapped by the visibility graph method. In our experiment, our algorithm achieves an average classification accuracy of 89.3%, an average sensitivity of 89.7%, an average specificity of 88.5%, and an average AUC of 0.947, which surpasses some state-of-the-art models trained on our data. In conclusion, our results indicate that the proposed method in this study could be effective and significance for massive screening of OSA patients in daily life. And our work provides an alternative framework for time series analysis.

Predeparture Flight Planning to Minimize Operating Cost for Urban Air Mobility

Urban air mobility (UAM) is envisioned to move to highly automated and high-density operations in low-altitude urban airspace in the future. Providers of services for UAM (PSU), rather than the legacy air traffic control, are anticipated to support operators with operational planning, aircraft deconfliction, conformance monitoring, and emergency information dissemination. Such services, for hundreds to thousands of simultaneous UAM operations in constrained airspace, can only be realized with automated systems. In this study, airspace and deconfliction models for generating predeparture conflict-free four-dimensional (4-D) flight trajectories are proposed, which can be further developed into an automated flight planning tool for PSU. A semistructured scalable airspace design for future UAM is proposed (i.e., a layered airspace topology with direct routes between vertiports, avoiding physical obstacles, such as buildings, obstructions, and restricted airspace) using the visibility graph method. Based on the proposed airspace design, deconfliction strategies (e.g., flight-level assignment and departure delay) are applied to obtain predeparture conflict-free 4-D trajectories of UAM operations by solving a mixed-integer programming problem, with the objective function to minimize the operating cost of UAM operations. Furthermore, sensitivity analysis is performed to investigate the impacts of three key cost parameters (electricity price, crew hourly rate, and maintenance hourly rate). The relationships of departure delay bound (maximum departure delay allowed) vs operating cost saving and departure delay bound vs delay cost to passengers are examined, as is the tradeoff between operating cost saving and passenger delay cost.

Visibility Graph Analysis of the Seismic Activity of Three Areas of the Cocos Plate Mexican Subduction Where the Last Three Large Earthquakes (M > 7) Occurred in 2017 and 2022.

The understanding of the dynamical behavior of seismic phenomena is currently an open problem, mainly because seismic series can be considered to be produced by phenomena exhibiting dynamic phase transitions; that is, with some complexity. For this purpose, the Middle America Trench in central Mexico is considered a natural laboratory for examining subduction because of its heterogenous natural structure. In this study, the Visibility Graph method was applied to study the seismic activity of three regions within the Cocos plate: the Tehuantepec Isthmus, the Flat slab and Michoacan, each one with a different level of seismicity. The method maps time series into graphs, and it is possible to connect the topological properties of the graph with the dynamical features underlying the time series. The seismicity analyzed was monitored in the three areas studied between 2010 and 2022. At the Flat Slab and Tehuantepec Isthmus, two intense earthquakes occurred on 7 and 19 September 2017, respectively, and, on 19 September 2022, another one occurred at Michoacan. The aim of this study was to determine the dynamical features and the possible differences between the three areas by applying the following method. First, the time evolution of the a- and b-values in the Gutenberg-Richter law was analyzed, followed by the relationship between the seismic properties and topological features using the VG method, the k-M slope and the characterization of the temporal correlations from the γ-exponent of the power law distribution, P(k) ∼ k-γ, and its relationship with the Hurst parameter, which allowed us to identify the correlation and persistence of each zone.

Convolutional neural network for screening of obstructive sleep apnea using snoring sounds

Screening and assessment for obstructive sleep apnea hypopnea syndrome (OSAHS) has attracted growing attention to improve the life of patients with sleep apnea. The gold standard for diagnosing OSAHS is an overnight polysomnography (PSG) in a dedicated sleep laboratory. Yet, the PSG test is professional, expensive and unsuitable for mass screening of the population. OSAH affects about 10 % of population in the world, and there are about 80 % suffers remaining undiagnosed. The automatic and cheap OSAHS patients screening methods are urgently needed. As a major sign of undiagnosed OSAHS, snoring has been used for diagnosis of OSAHS. An automated snore detection method would allow a faster diagnosis and more patients to be analyzed. In this paper, we build a database including more than 80 thousand of snoring sound episodes from 124 subjects. These sounds are recorded by non-contact microphone in the subject’s private room, and labeled by trained sleep clinicians. And then the visibility graph method is modified as a novel framework for encoding these snoring time series into images to fully take advantage of two-dimension convolutional neural networks (CNN) in computer vision tasks. At last, a CNN model based on visibility graph method (VG) is applied to automatically extract features and recognize severity of OSAHS based on these snoring sounds. The experimental results show that our approach achieves an accuracy of 92.5 %, sensitivity of 93.9 %, and specificity of 91.2 % for OSAHS recognition. Our research provides an alternative method for rapid and massive screening and diagnosis of OSAHS.

A symmetric adaptive visibility graph classification method of orthogonal signals for automatic modulation classification

AbstractVisibility graph methods allow time series to mine non‐Euclidean spatial features of sequences by using graph neural network algorithms. Unlike the traditional fixed‐rule‐based univariate time series visibility graph methods, a symmetric adaptive visibility graph method is proposed using orthogonal signals, a method applicable to in‐phase and quadrature (I/Q) orthogonal signals for adaptive graph mapping for radio modulated signals in automatic modulation classification tasks. The method directly models the intra‐channel and inter‐channel graph relations of I/Q signals using two different types of convolutional kernels. It captures non‐Euclidean spatial feature information of I/Q signals using a graph neural network combining graph sampling aggregation and graph differentiable pooling as a feature extractor. Extensive experimental results on two benchmark datasets and a simulated dataset containing channel fading show that the proposed Quadrature Signal Symmetric Adaptive Visibility Graph (QSSAVG) method in this paper outperforms the benchmark method in terms of classification accuracy and is also more robust against channel fading and noise variations.

Complexity parameters of solar-wind magnetic fluctuations at 1 AU during SC23 and SC24

Context. The solar wind develops a highly turbulent character during its expansion, where plasma and electromagnetic fluctuations coexist. Considering the presence of turbulence in the plasma as a complex system, the turbulence in the solar wind in general has been measured and studied using different techniques from a systems science point of view. These techniques provide the opportunity to obtain preliminary information even before much of the physics can be assimilated and integrated. Aims. We describe this plasma as a complex system in order to understand solar wind dynamics from a new perspective. Several missions provide a wide range of data concerning critical astrophysical phenomena. This poses a challenge to implement new effective methods to complement the characterization of the constantly new, and sometimes highly reduced information, especially when dealing with observational data with intermittent gaps. Methods. We work with magnetic fluctuation time series data obtained from the Wind mission at 1 AU in order to characterize the fast and slow solar wind behavior during solar cycles 23 (SC23) and 24 (SC24). We applied the horizontal visibility graph (HVG) method to obtain the evolution of measurements of Kullback-Leibler divergence (KLD), D, and the characteristic exponent, γ, over time. Both are complexity parameters extracted from the degree distributions of the networks. Results. By contrasting our complexity parameters, γ and D, with solar activity characterized by the number of sunspots and solar wind speed, we obtain significant intercorrelations among them during both cycles and ascending, descending, minimum, and maximum phases. According to γ values, the magnetic fluctuations of the solar wind are a correlated stochastic time series at 1 AU. Also, the divergence D recognizes SC23 as the most dissipative and identifies the slow wind as more variable than the fast wind, with a better anti-correlation in the minima phases. This study reveals that in terms of solar phases γmin > γdes > γasc > γmax, and Dmin < Ddes < Dasc < Dmax. We show that the HVG technique leads to results that are consistent with the complex nature of solar wind turbulence.

Characterizing the Solar Activity Using the Visibility Graph Method

In this paper, the Sun and its behavior are studied by means of complex networks. The complex network was built using the Visibility Graph algorithm. This method maps time series into graphs in which every element of the time series is considered as a node and a visibility criterion is defined in order to connect them. Using this method, we construct complex networks for magnetic field and sunspots time series encompassing four solar cycles, and various measures such as degree, clustering coefficient, mean path length, betweenness centrality, eigenvector centrality and decay exponents were calculated. In order to study the system in several time scales, we perform both a global, where the network contains information on the four solar cycles, and a local analysis, involving moving windows. Some metrics correlate with solar activity, while others do not. Interestingly, those metric which seem to respond to varying levels of solar activity in the global analysis, also do in the moving windows analysis. Our results suggest that complex networks can provide a useful way to follow solar activity, and reveal new features on solar cycles.

AUV Path Planning in Dynamic Environment Based on Improved Artificial Potential Field Method Based on Visibility Graph

In order to solve the forced shaking problem of the Autonomous Underwater Vehicle (AUV) facing dynamic obstacles in the path planning when the Artificial Potential Field Method is used, a method of removing the shaking state based on a favorable path is proposed, and on this basis, Visibility Graph Method is used to optimize the path of the AUV to avoid dynamic obstacles. By judging the relative motion direction of AUV and dynamic obstacle, the moving direction of AUV is adjusted based on Visibility Graph Method when it is far away from the obstacle. When it is close to the obstacle, the direction conducive to approaching the target point is selected as the favorable forward direction to bypass the obstacle. The simulation results show that the dynamic obstacle avoidance path optimization method based on the Visibility Graph Method reduces the number of moving steps by about 19% compared with the traditional method when dealing with a single dynamic obstacle, and can be applied in complex environments with multiple dynamic obstacles.

Evidence of self-organized criticality in time series by the horizontal visibility graph approach

Determination of self-organized criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. For this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for two numerical avalanche-based samples (i.e., sand-pile models), several financial markets, and a solar nano-flare emission model. These series are shown to have long-temporal correlations via the detrended fluctuation analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of the constructed HVGs and compare them with the values obtained for random and chaotic processes. The results manifest a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG’s features can distinguish between SOC and random systems.

Assessment of time irreversibility in a time series using visibility graphs.

In this paper, we studied the time-domain irreversibility of time series, which is a fundamental property of systems in a nonequilibrium state. We analyzed a subgroup of the databases provided by University of Rochester, namely from the THEW Project. Our data consists of LQTS (Long QT Syndrome) patients and healthy persons. LQTS may be associated with an increased risk of sudden cardiac death (SCD), which is still a big clinical problem. ECG-based artificial intelligence methods can identify sudden cardiac death with a high accuracy. It follows that heart rate variability contains information about the possibility of SCD, which may be extracted, provided that appropriate methods are developed for this purpose. Our aim was to assess the complexity of both groups using visibility graph (VG) methods. Multivariate analysis of connection patterns of graphs built from time series was performed using multiplex visibility graph methods. For univariate time series, time irreversibility of the ECG interval QT of patients with LQTS was lower than for the healthy. However, we did not observe statistically significant difference in the comparison of RR intervals time series of the two groups studied. The connection patterns retrieved from multiplex VGs have more similarity with each other in the case of LQTS patients. This observation may be used to develop better methods for SCD risk stratification.

Seizure detection algorithm based on fusion of spatio-temporal network constructed with dispersion index

Epilepsy is one of the common brain disorders. Traditional seizure detection is done by electroencephalography (EEG) technicians, which takes a lot of time. Therefore, this paper proposes a new method for automatic seizure detection. In this paper, we use multivariate variational mode decomposition (MVMD) method for modal decomposition of multi-channel EEG signals and introduce dispersion index (DI) as a new brain network weight calculation method which is based on dispersion entropy (DE) to extract the features of single-channel temporal brain network and multi-channel spatial brain network for seizure detection. In single-channel temporal brain network, the network is constructed by weighted horizontal visibility graph (WHVG) method which considers the sample points as network nodes. In multi-channel spatial brain networks, DI is used to calculate the correlation between channels and select the threshold to construct the ternary-valued network of channels. We perform the validation on two publicly available datasets. The results show that the classification results for F1, AUC, ACC, PRE, SEN and SPE on CHB-MIT dataset are 97.89%, 97.81%, 97.83%, 97.56%, 98.24% and 97.39%, respectively. In addition, the results for F1, AUC, ACC, PRE, SEN and SPE on Siena scalp dataset are 99.21%, 99.19%, 99.19%, 99.28%, 99.14%, and 99.24%, respectively. The method proposed in this paper achieves good results on both datasets. In general, the joint detection of temporal and spatial networks is promising, and DI can serve as a valid indicator of correlation.