Visibility Graph Research Articles

An analysis of the global fuel-trading market based on the visibility graph approach

Fuel is the cornerstone of a nation’s economy, and energy policy is a crucial part of national security. Therefore, it is very important to model and analyze the fuel trade. In this paper, a dynamic system by a visibility graph model is constructed to analyze time series data from the global fuel export trade. This paper analyses the fuel export trade of various countries, and the characteristics of fuel trade in different countries are identified by the visibility graph. According to the characteristics of the fuel export time series network, the examined countries are categorized, and the global fuel export market is divided into three groups. It has important guiding significance for understanding the global fuel market and formulating scientific fuel security policies.

AN EFFICIENT GRAPH THEORY-BASED ALGORITHM FOR SHIP TRAJECTORY PLANNING

The research presented in this paper is dedicated to the development of a path planning algorithm for a moving object in a dynamic environment. The marine environment constitutes the application area. A graph theory-based path planning method for ships is introduced and supported by the results of simulation tests and comparative analysis with a heuristic Ant Colony Optimization approach. The method defines the environment with the use of a visibility graph and uses the A* algorithm to find the shortest, collision-free path. The main contribution is the development of an effective graph theory-based algorithm for path planning in an environment with static and dynamic obstacles. The computational time does not exceed a few seconds. Obtained results allow to state that the method is suitable for use in an intelligent motion control system for ships.

İç mekân navigasyonu ağ modelleri: Karşılaştırmalı bir inceleme

Nowadays, the use of outdoor navigation applications is quite common. For indoor navigation, this case is still an emerging application due to the lack of use of a standardised positioning equipment, higher costs, accuracy issues, the more complex structure of indoor spaces and the fact that a comprehensive network model to support indoor navigation for floor-level paths and non-level paths and the studies on the computation of routes are not fully developed yet. Due to the degree of complexity of indoor spaces vary depending on the non-standard structures of buildings and the freedom of movement capability is in a wide spectrum, different navigation networks can be generated. In this study, the Medial Axis Transform (MAT) based methods and the Visibility Graph (VG) based network model that originates from isovists theory which are the prominent navigation network models in the literature are generated in the building information modelling of Yildiz Technical University Civil Engineering Faculty building by utilizing the two-dimensional floor plans of the building and a new approach is proposed based on the VG model by restricting the line of sight between sub-corridors of indoor space and combining it with the MAT. The usability of these navigation network models is compared in terms of the shortest distance and the fewest turns made on the route. The findings of the experimental study showed that the VG based network model which is shown in previous studies to be correlated with human perception enables a mean of 1.17 m shorter distances and 0.20 times fewer turns than the compared routes compared to closest network model. The statistical tests demonstrated that the proposed hybrid approach does not differ significantly from VG thus can be used instead of VG based model for various scenarios.

Efficient robotic path planning algorithm based on artificial potential field

<span lang="EN-US">Path planning is crucial for a robot to be able to reach a target point safely to accomplish a given mission. In path planning, three essential criteria have to be considered namely path length, computational complexity and completeness. Among established path planning methods are voronoi diagram (VD), cell decomposition (CD), probability roadmap (PRM), visibility graph (VG) and potential field (PF). The above-mentioned methods could not fulfill all three criteria simultaneously which limits their application in optimal and real-time path planning. This paper proposes a path PF-based planning algorithm called dynamic artificial PF (DAPF). The proposed algorithm is capable of eliminating the local minima that frequently occurs in the conventional PF while fulfilling the criterion of path planning. DAPF also integrates path pruning to shorten the planned path. In order to evaluate its performance, DAPF has been simulated and compared with VG in terms of path length and computational complexity. It is found that DAPF is consistent in generating paths with low computation time in obstacle-rich environments compared to VG. The paths produced also are nearly optimal with respect to VG.</span>

Novel Sensor/Access-Point Coverage-Area Maximization for Arbitrary Indoor Polygonal Geometries

Nowadays, sensor/access-point coverage is an essential problem for wireless communication and sensor systems, which will significantly impact the quality of access, monitoring, and surveillance. Indoor sensor/access-point placement still remains very challenging as the regions of interest (ROIs) or underlying geometries may be in an arbitrary polygonal shape. In this work, we would like to study how to place a sensor/access-point to maximize the coverage area within an arbitrary polygonal ROI. Our novel approach is based on finding the maximum-area clique over the visibility graph corresponding to the indoor geometry. According to many examples, our proposed optimal sensor/access-point scheme can lead to larger coverage efficiencies than the existing solution to the art gallery problem (AGP) and the conventional Delaunay triangulation method. Our new scheme is of great practical value as it can be applied for not only both convex and nonconvex simply-connected polygons but also both convex and nonconvex multiply-connected polygons with internal holes.

Socio-Spatial Relation in Small Island (Case Study: Karanrang Island, South Sulawesi, Indonesia)

Social interaction is an influential factor in shaping a community in a small island. There is a lack of study on how multi-ethnic groups of people living in a small island have shaped their community and maintained social harmony. This study identifies and analyzes the social interaction of residents in Karanrang Island in South Sulawesi, Indonesia. It focuses on how the social behavior of the residents has formed the spatial pattern of residential and community areas, including open spaces. Data of the residents' social behavior, activities, spatial layout of buildings, pathways, and major amenities were gathered from spatial mapping and on-site surveys. The analysis of socio-spatial patterns used the space syntax analysis method, namely Axial Analysis and Visibility Graph Analysis (VGA). The result shows that socio-spatial integration tends to occur in the irregular spatial configuration of residential areas, whereas socio-spatial segregation tends to occur in the regular spatial configuration. Furthermore, from the viewpoint of socio-spatial relation, the factors of activity location, residential density, and distance between houses significantly relate to social aspects such as community participation in social activities and willingness to assist neighbors. These findings are expected to provide consideration for the development of the socio-spatial structure that is suitable with the characteristics of small island communities, also to contribute to the sustainability of social order in the residential neighborhood of small islands.

Crash Diagnosis and Price Rebound Prediction in NYSE Composite Index Based on Visibility Graph and Time-Evolving Stock Correlation Network.

This study proposes a framework to diagnose stock market crashes and predict the subsequent price rebounds. Based on the observation of anomalous changes in stock correlation networks during market crashes, we extend the log-periodic power-law model with a metric that is proposed to measure network anomalies. To calculate this metric, we design a prediction-guided anomaly detection algorithm based on the extreme value theory. Finally, we proposed a hybrid indicator to predict price rebounds of the stock index by combining the network anomaly metric and the visibility graph-based log-periodic power-law model. Experiments are conducted based on the New York Stock Exchange Composite Index from 4 January 1991 to 7 May 2021. It is shown that our proposed method outperforms the benchmark log-periodic power-law model on detecting the 12 major crashes and predicting the subsequent price rebounds by reducing the false alarm rate. This study sheds light on combining stock network analysis and financial time series modeling and highlights that anomalous changes of a stock network can be important criteria for detecting crashes and predicting recoveries of the stock market.

The North–South Asymmetry of Sunspot Relative Numbers Based on Complex Network Technique

Solar magnetic activity exhibits a complex nonlinear behavior, but its dynamic process has not been fully understood. As the complex network technique can better capture the dynamics of nonlinear system, the visibility graphs (VG), the horizontal visibility graphs (HVG), and the limited penetrable visibility graphs (LPVG) are applied to implement the mapping of sunspot relative numbers in the northern and southern hemispheres. The results show that these three methods can capture important information of nonlinear dynamics existing in the long-term hemispheric sunspot activity. In the presentation of the results, the network degree sequence of the HVG method changes preferentially to the original data series as well as the VG and the LPVG, while both the VG and the LPVG slightly lag behind the original time series, which provides some new ideas for the nonlinear dynamics of the hemispheric asymmetry in the two hemispheres. Meanwhile, the use of statistical feature-skewness values and complex network visibility graphs can yield some complementary information for mutual verification.

Intelligent algorithm for dynamic functional brain network complexity from CN to AD

Alzheimer's disease (AD) is the main cause of dementia in the elderly. To date, it remains largely unknown whether and how dynamic characteristics of the functional networks differ from cognitively normal (CN) to AD. Here, we propose an AD dynamic network complexity intelligent detecting algorithm based on visibility graph. The focal regions that caused the dynamic abnormality of the connection mode were intelligently detected by creating a dynamic complexity network on the basis of the dynamic functional network. The results showed that the brain areas with different dynamic complexity gradually shifted from the frontal lobe to the temporal lobe and the occipital lobe. This was significantly related to the disorder of clinical patients from mood to memory and language. The increased dynamic complexity illustrates the compensatory effect of the brain area of AD lesions. In addition, the small-world topological properties of the dynamic complexity network have significant differences from CN to AD. To the best of our knowledge, this is the first time that such a concept is proposed. Our method of intelligently detecting the complexity of AD dynamic network provides new insights for understanding the internal dynamic mechanism of AD brain.

Automated sleep state classification of wide-field calcium imaging data via multiplex visibility graphs and deep learning

BackgroundWide-field calcium imaging (WFCI) allows for monitoring of cortex-wide neural dynamics in mice. When applied to the study of sleep, WFCI data are manually scored into the sleep states of wakefulness, non-REM (NREM) and REM by use of adjunct EEG and EMG recordings. However, this process is time-consuming and often suffers from low inter- and intra-rater reliability and invasiveness. Therefore, an automated sleep state classification method that operates on WFCI data alone is needed. New methodA hybrid, two-step method is proposed. In the first step, spatial-temporal WFCI data is mapped to multiplex visibility graphs (MVGs). Subsequently, a two-dimensional convolutional neural network (2D CNN) is employed on the MVGs to be classified as wakefulness, NREM and REM. ResultsSleep states were classified with an accuracy of 84% and Cohen’s κ of 0.67. The method was also effectively applied on a binary classification of wakefulness/sleep (accuracy=0.82, κ = 0.62) and a four-class wakefulness/sleep/anesthesia/movement classification (accuracy=0.74, κ = 0.66). Gradient-weighted class activation maps revealed that the CNN focused on short- and long-term temporal connections of MVGs in a sleep state-specific manner. Sleep state classification performance when using individual brain regions was highest for the posterior area of the cortex and when cortex-wide activity was considered. Comparison with existing methodOn a 3-hour WFCI recording, the MVG-CNN achieved a κ of 0.65, comparable to a κ of 0.60 corresponding to the human EEG/EMG-based scoring. ConclusionsThe hybrid MVG-CNN method accurately classifies sleep states from WFCI data and will enable future sleep-focused studies with WFCI.

Analysis of pulsating variable stars using the visibility graph algorithm.

We study the light curves of pulsating variable stars using a complex network approach to build visibility graphs. We consider various types of variables stars (e.g., Cepheids, δ Scuti, RR Lyrae), build two types of graphs (the normal visibility graph (VG) and the horizontal visibility graph (HVG)), and calculate various metrics for the resulting networks. We find that all networks have a power-law degree distribution for the VG and an exponential distribution for the HVG, suggesting that it is a universal feature, regardless of the pulsation features. Metrics such as the average degree, the clustering coefficient and the transitivity coefficient, can distinguish between some star types. We also observe that the results are not strongly affected by the presence of observation gaps in the light curves. These findings suggest that the visibility graph algorithm may be a useful technique to study variability in stars.

Equipment Layout Optimization Based on Human Reliability Analysis of Cabin Environment

There are many factors involved in the layout optimization of cabin equipment, and human factors should be considered in the early stage of layout design. Human reliability is an effective index to evaluate the probability of success of the human completion of tasks. In order to put forward the method of human reliability which is more suitable for the layout optimization of cabin equipment, the existing methods of human reliability analysis (HRA) are systematically studied. At the same time, taking HRA, equipment correlation and cabin balance as objective functions, the optimization problem of cabin equipment layout was quantified into a mathematical model. When solving the model, the visibility graph method was used to model the cabin path planning, and a solution platform for the optimization of cabin equipment layout was developed on the basis of a genetic algorithm. Finally, the developed platform was applied with a ship example, and the results before and after the layout optimization were displayed through a three-dimensional model. At the same time, equipment layout evaluation software was used to simulate the experimental results so as to compare the improvement of important parameters before and after the layout optimization.

Measuring the Topological Time Irreversibility of Time Series With the Degree-Vector-Based Visibility Graph Method

Time irreversibility of a time series, which can be defined as the variance of properties under the time-reversal transformation, is a cardinal property of non-equilibrium systems and is associated with predictability in the study of financial time series. Recent pieces of literature have proposed the visibility-graph-based approaches that specifically refer to topological properties of the network mapped from a time series, with which one can quantify different degrees of time irreversibility within the sets of statistically time-asymmetric series. However, all these studies have inadequacies in capturing the time irreversibility of some important classes of time series. Here, we extend the visibility-graph-based method by introducing a degree vector associated with network nodes to represent the characteristic patterns of the index motion. The newly proposed method is parameter-free and temporally local. The validation to canonical synthetic time series, in the aspect of time (ir)reversibility, illustrates that our method can differentiate a non-Markovian additive random walk from an unbiased Markovian walk, as well as a GARCH time series from an unbiased multiplicative random walk. We further apply the method to the real-world financial time series and find that the price motions occasionally equip much higher time irreversibility than the calibrated GARCH model does.

Nonlinear time series analysis of palaeoclimate proxy records

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability. In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These include approaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling. Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5 million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series. We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate. Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.

Visibility graph-based path-planning algorithm with quadtree representation

In recent years, unmanned surface vehicles (USVs) have been widely used in various applications. To fulfill target missions, USVs must be able to plan their path to the destination. Although many path-planning methods have been developed, most are inappropriate for application in complex marine environments. In this study, we propose a novel path-planning algorithm, which combines the merits of quadtree representation and visibility graphs, for efficient path planning of USVs in complex marine environments. Quadtree representation reduced the computation time and memory consumption. Additionally, the wind and wave data were considered to shorten the voyage time from the departure to destination points. Furthermore, the Dijkstra algorithm was applied to the quadtree to determine the suboptimal path. We then constructed a visibility graph with path waypoints using an improved line-of-sight algorithm to perform path planning on the visibility graph. The proposed algorithm not only facilitates path planning with minimum voyage time but also maintains the USV clearance distance from the coastline. To verify the performance, the proposed algorithm was compared with other methods for South Korean case studies. Overall, the proposed algorithm was able to generate a high-quality suboptimal path for the USV within a short time span.

A Bidirectional Interpolation Method for Post-Processing in Sampling-Based Robot Path Planning.

This paper proposes a post-processing method called bidirectional interpolation method for sampling-based path planning algorithms, such as rapidly-exploring random tree (RRT). The proposed algorithm applies interpolation to the path generated by the sampling-based path planning algorithm. In this study, the proposed algorithm is applied to the path created by RRT-connect and six environmental maps were used for the verification. It was visually and quantitatively confirmed that, in all maps, not only path lengths but also the piecewise linear shape were decreased compared to the path generated by RRT-connect. To check the proposed algorithm’s performance, visibility graph, RRT-connect algorithm, Triangular-RRT-connect algorithm and post triangular processing of midpoint interpolation (PTPMI) were compared in various environmental maps through simulation. Based on these experimental results, the proposed algorithm shows similar planning time but shorter path length than previous RRT-like algorithms as well as RRT-like algorithms with PTPMI having a similar number of samples.

An Efficient Sleep Scoring Method using Visibility Graph and Temporal Features of Single-Channel EEG.

This work proposes a method utilizing the fusion of graph-based and temporal features for sleep stage identification. EEG epochs are transformed into visibility graphs from which mean degrees and degree distributions are obtained. In addition, autoregressive model parameters, Higuchi fractal dimension, multi-scale entropy, and Hjorth's parameters are calculated. All these features extracted from a single EEG channel (Pz-Oz) are fed to an ensemble classifier called random undersampling with boosting technique. Two different approaches i.e. 10-fold crossvalidation and 50%-holdout are utilized to evaluate the performance of the model. Cross-validation accuracies of 91.0% and 97.3%, and kappa coefficients of 0.82 and 0.94 are achieved for 6- and 2-state classifications, respectively, which are higher than those of existing studies.Clinical relevance- Automatic and reliable sleep stage classification can reduce the burden of sleep experts in analyzing overnight sleep data (~ 8 hours). It can also assist them to find specific traits of interest such as spindle density, by providing annotated sleep data (hypnogram), thereby eliminating the need for tedious and expensive manual scoring. An accurate 2-state (wake/sleep) classification is also crucial for the patients with disorders of consciousness, where stimulation during wake state is considered more effective than that in sleep state.

Cuff-Less Blood Pressure Estimation via Small Convolutional Neural Networks.

Deep learning-based cuff-less blood pressure (BP) estimation methods have recently gained increased attention as they can provide accurate BP estimation with only one physiological signal as input. In this paper, we present a simple and effective method for cuff-less BP estimation by training a small-scale convolutional neural network (CNN), modified from LeNet-5, with images created from short segments of the photoplethysmogram (PPG) signal via visibility graph (VG). Results show that the trained modified LeNet-5 model achieves an error performance of 0.184±7.457 mmHg for the systolic BP (SBP), and 0.343±4.065 mmHg for the diastolic BP (DBP) in terms of the mean error (ME) and the standard deviation (SD) of error between the estimated and reference BP. Both the SBP and the DBP accuracy rank grade A under the British Hypertension Society (BHS) protocol, demonstrating that our proposed method is an accurate way for cuff-less BP estimation.

Brain functional networks analysis of five fingers grasping in virtual reality environment.

This study investigated the effects of different center of mass (COM) of the grasping device and visual time-delay on the information interaction between brain regions during five-finger grasping process. Nine healthy right-handed subjects used five fingers to grasp a special device in a virtual reality (VR) environment. Two independent variables were set in the experiment: the COM of the grasping device and the visual delay time. Place a 50 g mass randomly at five different directions of the grasping device base. The three levels of visual delay time appear randomly. The kinematics and dynamics and electroencephalogram (EEG) signals were recorded during the experiment. The brain network was constructed based on multiplex horizontal visibility graph (MHVG). Interlayer mutual information (MI) and phase locking value (PLV) were calculated to quantify the network, while clustering coefficient (C), shortest path length (L) and overall network efficiency (E) are selected to quantify the network characteristic. Statistical results show that when the mass is located in the radial side, during the load phase of grasping, the C and E is significantly higher than that in the proximal, ulnar and medial side, and L was significantly lower than that in the proximal and radial side. This shows that when grasping an object with a COM bias on the radial side, the process of brain feedforward control has higher level of information interaction and ability and it can build stronger sensorimotor memory. It is also found that the brain network features of theta, beta and gamma bands of EEG are positively correlated, especially between beta and gamma bands, which suggests there is a coupling relationship between different bands in information processing and transmission.Clinical Relevance- This study explains the neural mechanism of grasping control from the topological structure of the whole brain network level and the informatics.

Graph-domain features and their application in rotating machinery fault diagnosis

To more effectively extract the non-stationary and non-linear fault features of mechanical vibration signals, a novel fault diagnosis method for rotating machinery is proposed combining time-domain, frequency-domain with graph-domain features. Different from the conventional time-domain and frequency-domain features, the graph-domain features generated from horizontal visibility graphs can extract the fault information hidden in the graph topology. Aiming at the problem that too many features will lead to information redundancy, the Fisher score algorithm is applied to select several of sensitive features which are then fed into the support vector machine to diagnose the faults of rotating machinery. Experimental results indicate features extracted from the three domains can be used to obtain higher diagnosis accuracy than that extracted from any single domain or dual domains.