Horizontal Visibility Graph Algorithm Research Articles

The network structure of Sturmian sequences based on HVG

The horizontal visibility graph algorithm is a powerful tool to study time series. In this paper, we use this algorithm maps Sturmian sequences to complex networks and find that the degree sequences partly inherit the Sturmian character. Firstly, we prove that Sturmian sequences and their horizontal visibility graph (HVG) degree sequences can be generated separately by coding sequences. Then, using coding factors, we divide the Sturmian sequences of type 1 into six types and calculate the complexity functions of their HVG-degree sequences. Moreover, we show that the HVG-degree sequences of Sturmian sequences of type 0 are the same Sturmian sequence. Finally, we use the complexity functions of HVG-degree sequences to uniquely characterize the Sturmian sequences.

Multiple fault diagnosis for rolling bearings method employing CEEMD-GCN based on horizontal visibility graph

Multiple faults often occur in the operation of rotating machinery transmission systems. The fault signals of multiple bearings interfere with each other, which makes feature extraction and diagnosis of complex compound fault signals difficult. Because the graph convolution networks (GCN) can effectively map the structural information from complex data and its model has a certain generalization ability, this paper proposes a multiple fault diagnosis method for rolling bearings employing complete ensemble empirical mode decomposition (CEEMD) and a GCN (CEEMD-GCN) based on a horizontal visibility graph (HVG). Firstly, in order to highlight the effective feature information in the multiple fault signal and reduce noise interference, multiple indicators of correlation and kurtosis are used to reconstruct the decomposed signals through CEEMD; secondly, the reconstructed signals are constructed as an HVG, and the HVG maps the time series signal to the graphic structure data, reflecting the local geometric characteristics of the vibration signal through the horizontal visibility relationship; finally, taking the signal samples obtained by the HVG algorithm as the input data of the model, the GCN model is trained to realize the diagnosis of multiple faults. The experimental results show that the presented methodology is superior to other methods and exhibits generalization ability for multiple fault diagnosis.

Nonlinear correlations in multifractals: Visibility graphs of magnitude and sign series.

Correlations in a multifractal series have been investigated extensively. Almost all approaches try to find scaling features of a given time series. However, the scaling analysis has always been encountered with some difficulties. Of particular importance is finding a proper scaling region and removing the impact of the probability distribution function of the series on the correlation extraction methods. In this article, we apply the horizontal visibility graph algorithm to map a stochastic time series into networks. By investigating the magnitude and sign of a multifractal time series, we show that one can detect linear as well as nonlinear correlations, even for situations that have been considered as uncorrelated noises by typical approaches such as the multifractal detrended fluctuation analysis. Furthermore, we introduce a topological parameter that can well measure the strength of nonlinear correlations. This parameter is independent of the probability distribution function and calculated without the need to find any scaling region. Our findings may provide new insights about the multifractal analysis of a time series in a variety of complex systems.

A complex network analysis of inbound tourism in Sicily

AbstractIn this article, the complex dynamics of inbound tourism in Sicily is analyzed for the period 1998–2017. The horizontal visibility graph algorithm is used to transform the overnight stays' time series into a network whose topology is investigated by standard network analysis. Discontinuities in the domestic and international tourism demand were identified in order to detect signals of change and the timing of the directional change in tourism growth. The network degree distribution confirms the complex structure of the destination and reveals the random and thus more unpredictable nature of the international tourism demand in Sicily, compared with a more stable domestic segment. Some policy implications are drawn.

Creation of language networks based on texts with using visibility graphs algorithms

A method to constructing language networks is proposed. Key words and concepts from the set of documents which describe some subject domain are retrieved. Numeric values are assigned to each word using a TF-IDF metric, that is intended to reflect how important a word is to a document in a collection or corpus. As the result a time series are constructed. A tool in time series analysis – the visibility graph algorithm is used for constructing the graph of subject domain. In this article two actual subject domains (“Space” and “Computer graphic”) are considered for example. The proposed method is used for the set of documents, which are related with “Space” and “Computer graphic”. A network of connections between terms and concepts, which go into textual documents is builded. Building networks of words, the nodes of which are elements of the text, enables to reveal key components of the text. At the same time, the task of determining the important structural elements of the text which are also informationally important, is actual. As a result of the research, it was found that such words as “uranium”, “nuclear”, “waste”, “Jupiter”, “Mercury”, “Moon”, “Earth”, “comet”, “space” and others are key for the subject area “Space”. This article shows that applying only a TF metric is more expedient compared with the TF-IDF metric in case when the set of documents describe one subject domain. Also the results of applying the visibility graphs algorithm and the compactified horizontal visibility graph algorithm are compared. It was found that in some case using the compactified horizontal visibility graph algorithm gives a network of words with more quantity of connections between concepts compared with using the visibility graphs algorithm. An open-source visualization and exploration software for all kinds of graphs and networks Gephi and an original package of specially developed Python modules are used for simulation and visualization as an additional tool. The proposed method can be used for visualization some subject domain, and also for information decision support systems, enabling to reveal key components of a subject domain. Also the results of this article can be used for building UI of information retrieval systems, enabling to make a process of search a relevant information easier.

Метод побудови і використання семантичних моделей для моніторингу суспільної думки

It is proposed a method for constructing and using semantic models (SM) for the purpose of continuous monitoring of public opinion, opinion mining (OM). Under the semantic model in the framework of this work, it is implied the subject domain model, which has the form of a directed graph, the vertices of which correspond to the concepts of the domain, and the arcs define the relations between them. Semantic models make it possible to use the results of linguistic statistical analysis of texts (Text Mining) and the use of Information Extraction methods contained in texts from the Internet for opinion mining. While the existing public opinion analysis projects are more focused on one-time (static) public opinion research on objects and phenomena, it is proposed a method for automated construction and use of SM based on continuous monitoring of public opinion on the Internet. The OM procedure consists of three steps: the construction and clustering of the SM; selection of documents and the sentiment definition of topics; visualization of results. The SM construction using the compactified horizontal visibility graph algorithm, the use of cluster analysis methods for determining relevant topics, estimating the proportion and tonality of individual sub-themes in the overall thematic information flow is shown. As examples, the models of subject areas corresponding to the topics: «One Belt, One Road», «Nord Stream», «Genetically Modified Organisms» are examined. The obtained results confirm the possibility of using the proposed method of opinion monitoring in various subject areas.

The novel multi-scale local irreversibility analysis method based on segmentation about time series

In this paper, we mainly study the local irreversibility of time series. For this purpose, inspired by the idea of segmentation contained in multi-fractal detrended fluctuation analysis, we propose a novel time series irreversibility analysis, that is, multi-scale local irreversibility method based on the segmentation. By means of this method, we can availably discuss the fluctuation of local irreversibility of a time series as the timescale changes. In order to explore the performance of this method in analyzing the local irreversibility of time series in depth, we provide the definition of Kullback–Leibler distribution (KLD) combined with the horizontal visibility graph algorithm, which has been verified to be an intuitive method for the analysis of irreversibility. Meanwhile, we also introduce three other irreversible indices: Porta’s, Guzik’s and Ehler’s indices ($$P\%$$, $$G\%$$ and E, respectively) for deeper detection. Further on, we first apply the above methods to the simulated time series generated by the auto-regressive fractionally integrated moving average model and financial time series. By virtue of the new multi-scale local irreversibility analysis method, the results show that KLD and Ehler’s index are superior to the other two measures when comparing the difference of local irreversibility of different time series. At the same time, we also find an interesting phenomenon, that is, results of Porta’s index are similar to those of Guzik’s index and both of them can better expose the similarity of local irreversibility of different time series. Besides, all of them can exhibit their powerful function in analyzing the relationship of the holistic and local irreversibility of a time series. As a further validation, we specially examine effect of the new method on the analysis to different electrocardiogram signals. The results provide us with plenty of meaningful results, which are consequential for disease detection.

New irreversibility measure and complexity analysis based on singular value decomposition

Visibility graph algorithm is a powerful tool for visualization and analysis of complex dynamical system. Kullback–Leibler divergence(KLD), based on the horizontal visibility graph algorithm, has received largely extensive attention in the field of irreversibility analysis. In this paper, we will propose a new irreversibility measure built on the multi-scale theory, i.e. the KLD based on singular value decomposition(KLD-SVD). Furthermore, since matrix singular value can reflect the basic characteristics of the complex system, we further bring forward the definition of Shannon entropy with singular value decomposition(SE-SVD) after considering that the Shannon entropy has been well defined as a complexity measure. In order to show the advantages of these two new measures in detecting the complexity of systems, several simulation and real data experiments are chosen to examine the performance of them. Through these results, we find that the average and variance of KLD-SVD corresponding to each time series is less than that of the KLD. Moreover, KLD-SVD’s volatility is significantly weaker than KLD’s. As there is a conceptual link between predictability and irreversibility, we can argue that KLD-SVD algorithm implies the higher predictability and lower confusion. On the other hand, SE-SVD can do well in revealing the internal complexity of the different time series. Meanwhile, it is useful to mention that SE-SVD is robust against noise efficiently.

Assessment of visibility graph similarity as a synchronization measure for chaotic, noisy and stochastic time series

Finding synchronization between the outputs of a dynamic system, which are represented mostly as time series, helps to characterize the system activities during an occurrence. An important issue in analyzing time series is that they may behave chaotically or stochastically. Therefore, applying a reliable synchronization measure which can capture the dynamic features of the system helps to quantify the interdependencies between time series, correctly. In this paper, we employ similarity measures based on visibility graph (VG) algorithms as an alternative and radically different way to measure the synchronization between time series. We assess the performance of VG-based similarity measures on chaotic, noisy and stochastic time series. In our experiments, we use the Rössler system and the noisy Hénon map as representative instances of chaotic systems, and the Kuramoto model for studying detection of synchronization between stochastic time series. Our study suggests that the similarity measure based on the horizontal VG algorithm should be favored to other measures for detecting synchronization between chaotic and stochastic time series.

Complexity traits and dynamics of tourism destinations

This paper is rooted in network science and contributes to filling two gaps, developing multiple case studies in order i) to measure the complex structure of tourism destination and ii) to explore its evolution over time, by mapping turning points. The findings put forward ten new analyses, allowing the research team to test two hypotheses: i) concerning the complex structure, the tendency of tourism destinations to remain far from the chaos threshold, ii) concerning turning points, the ability of different destinations to show also different evolution through time. The paper uses the Horizontal Visibility Graph Algorithm and applies it to a sample of ten tourism destinations in the second leading Italian tourism region per size: Trentino-Alto Adige. Findings confirm both hypotheses. Limitations and research implications are drawn.

Mapping time series into networks as a tool to assess the complex dynamics of tourism systems

This paper contributes to filling two gaps: i) the presence of a limited amount of studies focused on tourism demand turning points, ii) the prevalent recourse to linear models in demand analysis, disregarding the complex structure of tourism destinations. The paper uses the Horizontal Visibility Graph Algorithm, a technique able to transform a time series of observations into a network whose topology preserves some fundamental characteristics of the system examined. The empirical work focuses on Livigno, an Italian alpine destination.Findings reveal four turning points in the last 50 years; these changes are built around shifts in the origin market segments. The network's degree distribution confirms the complex structure of the destination and reconfirms the importance of non-linear models and methods for the analysis of tourism demand.