Limited Penetrable Visibility Graph Research Articles

Sliding limited penetrable visibility graph for establishing complex network from time series.

This study proposes a novel network modeling approach, called sliding window limited penetrable visibility graph (SLPVG), for transforming time series into networks. SLPVG takes into account the dynamic nature of time series, which is often affected by noise disturbances, and the fact that most nodes are not directly connected to distant nodes. By analyzing the degree distribution of different types of time series, SLPVG accurately captures the dynamic characteristics of time series with low computational complexity. In this study, the authors apply SLPVG for the first time to diagnose compensation capacitor faults in jointless track circuits. By combining the fault characteristics of compensation capacitors with network topological indicators, the authors find that the betweenness centrality reflects the fault status of the compensation capacitors clearly and accurately. Experimental results demonstrate that the proposed model achieves a high accuracy rate of 99.1% in identifying compensation capacitor faults. The SLPVG model provides a simple and efficient tool for studying the dynamics of long time series and offers a new perspective for diagnosing compensation capacitor faults in jointless track circuits. It holds practical significance in advancing related research fields.

Motion states identification of underwater glider based on complex networks and graph convolutional networks

Underwater glider (UG) plays an important role in ocean observation and exploration for a more efficient and deeper understanding of complex ocean environment. Timely identifying the motion states of UG is conducive for timely attitude adjustment and detection of potential anomalies, thereby improving the working reliability of UG. Combining limited penetrable visibility graph (LPVG) and graph convolutional networks (GCN) with self-attention mechanisms, we propose a novel method for motion states identification of UG, which is called as visibility graph and self-attention mechanism-based graph convolutional network (VGSA-GCN). Based on the actual sea trial data of UG, we chose the attitude angle signals of motion states related sensors collected by the control system of UG as the research object and constructed complex networks based on the LPVG method from pitch angle, roll angle, and heading angle data in diving and climbing states. Then, we build a self-attention mechanism-based GCN framework and classify the graphs under different motion states constructed by a complex network. Compared with support vector machines, convolutional neural network, and GCN without self-attention pooling layer, the proposed VGSA-GCN method can more accurately distinguish the diving and climbing states of UG. Subsequently, we analyze the variation of the transitivity coefficient corresponding to these two motion states. The results suggest that the coordination of the various sensors in the attitude adjustment unit during diving becomes closer and more efficient, which corresponds to the higher network measure of the diving state compared to the climbing state.

Generalized limited penetrable vector visibility graph

The paper introduced a new way for converting the multivariate time series to complex network combining the vector visibility graph and limited penetrable theory, and the concept is discussed on the generalized limited penetrable range, termed as generalized limited penetrable vector visibility graph. The proposed method is verified by the Lorenz system. We use the four kinds of network structure characteristic to evaluate the noise resistance of the method quantitatively, and provide the strategy with guidance for choosing the optimal limited penetrable range. The results show that the limited penetrable vector visibility graph inherits the noise resistance of limited penetrable visibility graph in the multivariate time series analysis. The generalized limited penetrable range is discussed to clarify the effect on the network structure.

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

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.

CLPVG: Circular limited penetrable visibility graph as a new network model for time series.

A visibility graph transforms time series into graphs, facilitating signal processing by advanced graph data mining algorithms. In this paper, based on the classic limited penetrable visibility graph method, we propose a novel mapping method named circular limited penetrable visibility graph, which replaces the linear visibility line in limited penetrable visibility graph with nonlinear visibility arc for pursuing more flexible and reasonable mapping of time series. Tests on degree distribution and some common network features of the generated graphs from typical time series demonstrate that our circular limited penetrable visibility graph can effectively capture the important features of time series and show higher robust classification performance than the traditional limited penetrable visibility graph in the presence of noise. The experiments on real-world time-series datasets of radio and electroencephalogram signals also suggest that the structural features provided by a circular limited penetrable visibility graph, rather than a limited penetrable visibility graph, are more useful for time-series classification, leading to higher accuracy. This classification performance can be further enhanced through structural feature expansion by adopting subgraph networks. All of these results demonstrate the effectiveness of our circular limited penetrable visibility graph model.

Activity recognition using multiplex limited penetrable visibility graph

To solve the dynamic problem of different activities in human activity recognition research, an activity recognition method based on a multiplex limited penetrable visibility graph is proposed. The 21 pressure values for each sampling are mapped to nodes in the first-layer network; then the average path length of nodes in the asynchronous periodic network is obtained, and the second-layer network used to explore different activities is built. Finally, the characteristic parameters and dynamic characteristics of different activities are explored and analyzed. The experimental results demonstrate that through the joint distribution of the average clustering coefficient and the maximum degree parameter of the node, the discrimination problems of different postures can be better realized, and it has good adaptability. It provides a new approach to gait recognition research that can be used in medical clinical diagnosis, rehabilitation training, and public health.

Weighted multi-scale limited penetrable visibility graph for exploring atrial fibrillation rhythm

Atrial fibrillation (AF) is a common cause of serious diseases such as stroke, heart failure and coronary artery disease, and electrocardiogram (ECG) detection is an important means of identifying AF. However, the ECG signal is quite noisy, making it difficult to detect AF through this method. Removing noise interference in ECG signals is a challenging problem. Traditional methods usually adopt various filtering methods to tackle this problem. Inspired by complex network theory, in this paper we present an innovative denoising approach for ECG detection called weighted multi-scale limited penetrable visibility graph (WMS-LPVG), which allows us to detect the rhythms characterizing AF in noisy ECG signals. To our knowledge, this is the first model that represents the AF rhythm series from the perspective of multi-scale complex networks. Furthermore, our WMS-LPVG model characterizes the AF rhythms in more detail, enabling us to identify AF sufferers more accurately. To demonstrate the effectiveness of our WMS-LPVG method, we first propose a new concept, called local efficiency entropy (LEE), which is utilized to identify the dynamic characteristics of time series. We then study the LEE-fluctuation trend under different scale factors. The experimental results show that the proposed LEE criterion can identify four kinds of ECG waveforms at a large scale. We then fuse the extracted LEE features with the original sequential features of ECG signals to build a multi-model complex network and feed the fused features into an XGboost model to identify AF patients. To demonstrate the generality of our WMS-LPVG model, we construct complex networks with WMS-LPVG for periodic and chaotic time series, respectively, and further discuss their degree distributions. The results show that our WMS-LPVG method perfectly retains information about original sequences and offers good anti-noise ability.

Automatic radar antenna scan type recognition based onlimited penetrable visibility graph

To address the problem of the weak anti-noise and macro-trend extraction abilities of the current methods for identifying radar antenna scan type, a recognition method for radar antenna scan types based on limited penetrable visibility graph(LPVG) is proposed. Firstly, seven types of radar antenna scans are analyzed, which include the circular scan, sector scan, helical scan, raster scan, conical scan, electromechanical hybrid scan and two-dimensional electronic scan. Then, the time series of the pulse amplitude in the radar reconnaissance receiver is converted into an LPVG network, and the feature parameters are extracted. Finally, the recognition result is obtained by using a support vector machine (SVM) classifier. The experimental results show that the recognition accuracy and noise resistance of this new method are improved, where the average recognition accuracy for radar antenna type is at least 90% when the signal-to-noise ratio (SNR) is 5 dB and above.

Multi-Function Radar Signal Sorting Based on Complex Network

In complex electromagnetic environments, the challenge of signal sorting task for multi-function radars (MFRs) with various work modes has arisen. The previous methods are prone to cause the so-called “increasing batch” problem, which means that the work modes of one MFR may be sorted into multiple emitters. In this letter, a MFR signal sorting method based on complex network is proposed to tackle the problem mentioned above. The novel method utilizes limited penetrable visibility graph to construct the network from interleaved radar pulse sequences, then employs label propagation algorithm and density peak clustering to detect community structures, thus fulfilling deinterleaving of pulses from several MFRs. Simulation results show that the proposed method is effective to alleviate the “increasing batch” problem, and is also robust under non-ideal conditions.

Multilayer limited penetrable visibility graph for characterizing the gas-liquid flow behavior

The research of the dynamical flow behavior of gas-liquid two-phase flow remains a challenge of great importance. We first carry out the vertical upward gas-liquid two-phase flow experiment in a 50 mm inner-diameter pipe and capture flow information via four-sector distributed conductance sensor. Then, we develop multilayer limited penetrable visibility graph (MLPVG) to analyze multichannel measurements, aiming to characterize the complicated flow behavior. We calculate two projection networks of MLPVG from two different perspectives (i.e. the overlapping information and the whole information). The ratio between the global clustering coefficients of these two projection networks is calculated as a quantitative indicator to characterize the multilayer network. We find that the proposed multilayer network measure can effectively characterize the evolution of gas-liquid flow, from randomly dispersed bubbles to periodically arisen gas slugs. The results suggest that our method can effectively fuse multichannel measurements and reveal the evolution of the complicated flow behavior.

A Graph-Temporal Fused Dual-Input Convolutional Neural Network for Detecting Sleep Stages from EEG Signals

Sleep is an essential integrant in everyone's daily life. Thereby, it is an important but challenging problem to construct a reliable and stable system, that can monitor user's sleep quality automatically. In this brief, we combine complex network and deep learning to propose a novel Graph-Temporal fused dual-input Convolutional Neural Network (CNN) method to detect sleep stages by using the Sleep-EDF database. Firstly, we segment each single-channel EEG signal into non-overlapping 30s epochs to set up the network. For that, we map each epoch into a Limited Penetrable Visibility Graph (LPVG) and obtain the corresponding Degree Sequence (DS) by calculating the node degree. Finally, the DSs and the 30s EEG epochs are combined as inputs of the novel Graph-Temporal fused dual-input CNN to learn about the graph topology and about the temporal feature representations of the raw data for the purpose of classifying the sleep stages into the two-, three-, four-, five-, and six-state. Notably, the classification accuracy of six-state stage detection is 87.21% and the corresponding Kappa value is 0.80. The results demonstrate the effectiveness of our model structure in detecting sleep states, whereby they further provide a basic strategy for future sleep research.

Construction of Multiplex Muscle Network for Precision Pinch Force Control.

Muscle synergy is a fundamental mechanism of motor control. Despite a number of studies focusing on muscle synergy during power grip and pinch at high-level force, relatively less is known about the functional interactions between muscles within low-level force production during precision pinch. Traditional analytical tools such as nonnegative matrix factorization or principal component analysis have limitations in processing nonlinear dynamic electromyographic signals and have confined sensitivity particularly for the low-level force production. In this study, we developed a novel method - multiplex muscle networks, to investigate the dynamical coordination of muscle activities at low-level force production during precision pinch. The multiplex muscle network was constructed based on multiplex limited penetrable horizontal visibility graph (MLPHVG). Seven forearm and hand muscles, including brachioradialis (BR), flexor carpi ulnaris (FCU), flexor carpi radialis (FCR), flexor digitorum superficialis (FDS), extensor digitorum communis (EDC), abductor pollicis brevis (APB) and first dorsal interosseous (FDI), were examined using surface electromyography (sEMG). Eight healthy subjects were instructed to perform a visuomotor force tracking task by producing higher (10% MVC) and lower (1% MVC) precision pinch. Interlayer mutual information I, average edge overlap ω weighted clustering coefficient CW, weighted characteristic path length LW were selected as network metrics. We assessed the undirected weighted network generated from multiplex muscle network after taking the I between paired muscle network layers as edge. There are significant differences between higher and lower force level with higher I, ω, CW and lower LW at higher force level. Advanced efficiency of information processing in the regional and global perspective indicated dynamical alterations when human faces the higher force tracking task. It suggested that ω may be an important characteristic to classify different force control states with the average classification accuracy of 82.21%. These findings reveal related alterations of functional interactions between muscles involved in precision pinch. The novel method for constructing multiplex muscle network may provide insights into muscle synergies during precision pinch force control.

Analysis of Gas-water Flow Transition Characteristics Based on Multiscale Limited Penetrable Visibility Graph

It’s a significant challenge for gas-water flow transition characteristics from experimental measurements in the study of multiphase flow systems. The limited penetrable visibility graph has been proved to be an efficient methodology for revealing nonlinear dynamical behaviors of time series. In order to uncovering gas-water flow transitions, gas-water flow experiment was carried out to obtain time series signals related to the transitions of three flow patterns. Then a novel multiscale limited penetrable visibility graph (MLPVG) is used to construct complex networks from many different experimental flow conditions. The multiscale network measures associated with node degree are employed to describe the topological features of the constructed MLPVG. The results show that the multiscale limited penetrable visibility graph can not only effectively characterize flow transition but also yields novel insights into the identification of gas-water flow patterns.

Classification of EEG Signals on VEP-Based BCI Systems With Broad Learning

Brain–computer interface (BCI) systems based on electroencephalography (EEG) signals have been extensively used in medical practice. To enhance the BCI performance, improving the classification accuracy of EEG signals is the key, which has always been the focus of research and development. In this article, a novel method integrating complex network and broad learning system (BLS) is proposed for visual evoked potential (VEP)-based BCI research. First, systematic VEP-based brain experiments are conducted for obtaining EEG signals, including steady-state VEP (SSVEP) and steady-state motion VEP (SSMVEP). Then, limited penetrable visibility graph (LPVG) and its degree sequence are employed to implement the preliminary feature extraction. All these features are finally fed into a BLS to study and classify the SSVEP and SSMVEP signals, respectively. The classification results show that our LPVG-based BLS can effectively classify VEP-based EEG signals, with average classification accuracy 96.22% for SSVEP and 74.54% for SSMVEP. These results are significantly better than other comparison methods as well as traditional CCA-based methods. All these open up new venues for studying EEG-based BCI systems via the fusion of network science and BLS.

Sequential limited penetrable visibility-graph motifs

Network motif provides a powerful tool to characterize the recurrent and statistically significant microstructure of networks. We in this paper develop the sequential motifs in limited penetrable visibility graph and introduce the motif entropy as the quantitative index to estimate the complexity of network structure. The visibility-graph motif entropy and limited penetrable visibility-graph motif entropy of graphs associated with chaotic time series and fractional Brownian motion are studied. The results suggest that limited penetrable visibility-graph motif entropy presents the better robustness than visibility-graph motif entropy and potential ability in distinguishing different time series. In the end, the limited penetrable visibility-graph motif entropy and visibility-graph motif entropy are applied to mine the information about different flow patterns contained in the ultrasonic sensor signals of oil-in-water two-phase flow.

Analyzing dynamic association of multivariate time series based on method of directed limited penetrable visibility graph

In order to study the characteristics of the evolution behavior of the relationship among multivariate time series, this paper proposes a method of constructing Multivariate Time Series-Dynamic Association Network (MTS-DAN) which represents multivariate time series associated relationship in the specific period. Firstly, we adopt transfer entropy algorithm to measure the associated relationship among multivariate time series. Secondly, the temporal behavior of the relationship is constructed into a complex network by the directed limited penetrable visibility graph (DLPVG) method. Thirdly, we explore the potential patterns of multivariate time series according to the physical characteristics of the network. Artificially generated data, SST and financial time series data are as sample separately in this paper. The experimental results reveal some statistical evidences that the associated relationship among multivariate time series is in a dynamic evolution process. There are association patterns among multivariate time series and a few types of patterns play a significant role in the process, while the clustering effect appears in the long-term evolution process. Furthermore, the results also show that multivariate time series have a close relation with actual events, which indicates that the method is of great significance to the research and prediction of events.

A directed limited penetrable visibility graph (DLPVG)-based method of analysing sea surface temperature

ABSTRACTThe present paper studies the dynamic association among the sea surface temperature (SST) data through directed limited penetrable visibility graph (DLPVG) method. We analyse the fluctuation trend of temperature in different regions by constructing an SST-dynamic association network to explore the topology structure. By analysing the SST data of the East China Sea, we find that there are association patterns among multivariate SST and a few types of patterns play a significant role in the movement of the sea water. Furthermore, the experiments also show that the multivariate SST has a close relationship with El Niño events, which indicates that the network is of great significance to the research and prediction of the El Niño phenomenon.

Dynamic evolution characteristics of European union emissions trade system price from high price period to low price period

Carbon market is a valid measure for promoting green and low-carbon development, and price is the core of market mechanism. In this work, combining directed limited penetrable visibility graph and coarse graining method, a new method is proposed to identify the potential periods and dynamic evolution characteristics of carbon price, which opens up a new perspective for government and investors to understand evolution characteristics and prevent risks. At the same time, a empirical analysis is conducted based on EU ETS daily price from September 29, 2009 to September 29, 2017, and the dynamic fluctuation characteristics of carbon price from high price period to low price period are obtained.

Locally Weighted Adjustable Parameter-Based LPVG in the Identification of Functional Regions

Mobile users’ online traffic records are a type of data that are closely related to human activities. To explore the differences in lifestyles of Internet users, online records of base stations expressed as time series need to be classified. However, due to the circadian rhythms, such time series have the same trend and small-scale local differences. Traditional similarity measurement using original time series is difficult to adequately capture local features of time series. By mapping the time series into visibility graph, the similarity measurement in the graph domain is obtained preserving the dynamic structure and local features to the greatest extent. In this paper, a locally weighted adjustable parameter-based limited penetrable visibility graph (LWAPLPVG) is proposed to further improve the noise resistance of visibility graph and local identification of limited penetrable visibility graph. We get APLPVG by modifying the visibility criteria, which has noise resistance while preserving local features as well. Simple measurement, such as degree sequence in graph domain, is extracted and proved, which is able to amplify small-scale differences. By considering the circadian rhythms of cyclical and trend time series, APLPVG is weighted locally. We use a real dataset of usage detail records (UDRs) to verify that LWAPLPVG can better improve the identification of time series of functional regions with noise resistance.

Epileptic seizure detection based on The Limited Penetrable visibility graph algorithm and graph properties

Introduction: Epileptic seizure detection is a key step for both researchers and epilepsy specialists for epilepsy assessment due to the non-stationariness and chaos in the electroencephalogram (EEG) signals. Current research is directed toward the development of an efficient method for epilepsy or seizure detection based the limited penetrable visibility graph (LPVG) algorithm.   Materials and Methods: Single channel EEG signals are mapped into the LPVGs and then 14 features are calculated from these graphs. Then some features are selected using Sequential forward feature selection method and given to error-correcting output codes (ECOC) to classify signals into three groups of healthy, seizure free (interictal) and during a seizure (ictal) groups. Results: Experimental results show our method can classify normal, ictal and interictal groups with a high accuracy of 96.31%. Conclusion: The proposed method is fast and easy. Comparison the performance of the proposed method with other automatic seizure detection method also shows our method has better performance.