From time series to complex networks: The phase space coarse graining

Wang, Minggang; Li, Tian

doi:10.1016/j.physa.2016.06.028

Cited by 78 publications

(32 citation statements)

References 40 publications

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“…Several methodologies for understanding the complicated behavior of nonlinear time series have been recently developed, including chaos analysis [1], fractal analysis [2], and complexity measurement [3]. With the development of complex network theories [4][5][6][7], a new multidisciplinary methodology for characterizing nonlinear time series using complex network science has emerged and rapidly expanded [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The main tool of these methods is to use an algorithm or algorithms to transform a nonlinear time series into a corresponding complex network and then use the topological structure of complex networks to analyze the properties of the nonlinear time series.…”

Section: Introductionmentioning

confidence: 99%

“…Gao et al [14] proposed a limited penetrable visibility method (LPVG) and multiscale limited penetrable horizontal visibility graph (MLPHVG). The third one is the phase space reconstruction method [15][16]. It begins with a phase space reconstruction of time series analysis, maps fixed-length time series segments into nodes of a network, and then uses the correlation coefficients (or distances) between these nodes to determine whether they are connected or not.…”

Section: Introductionmentioning

confidence: 99%

“…Although there have been abundant empirical results obtained using time series complex network algorithms [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], rigorous theoretical results are still lacking. Only a small amount of literature [9][10][11][12] has presented exact results on the properties of the horizontal visibility graphs (HVG) associated with random series.…”

Section: Introductionmentioning

confidence: 99%

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Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

Wang

Vilela

et al. 2018

Sci Rep

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The limited penetrable horizontal visibility algorithm is an analysis tool that maps time series into complex networks and is a further development of the horizontal visibility algorithm. This paper presents exact results on the topological properties of the limited penetrable horizontal visibility graph associated with independent and identically distributed (i:i:d:) random series. We show that the i.i.d: random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution, independent of the probability distribution from which the series was generated. We deduce the exact expressions of mean degree and clustering coefficient, demonstrate the long distance visibility property of the graph and perform numerical simulations to test the accuracy of our theoretical results. We then use the algorithm in several deterministic chaotic series, such as the logistic map, H´enon map, Lorenz system, energy price chaotic system and the real crude oil price. Our results show that the limited penetrable horizontal visibility algorithm is efficient to discriminate chaos from uncorrelated randomness and is able to measure the global evolution characteristics of the real time series.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

Wang

Vilela

et al. 2018

Sci Rep

Self Cite

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“…In this paper, we introduce complex network theory to present the complex interaction behavior of large-scale network traffic flows. Since complex network provides a powerful mechanism for capturing the interactive relationships among study objects, it has been an effective method for relational expression of structured datasets [4,5,6], especially the time series data. For instance, in the study of earthquake time series the authors [7,8] developed the earthquake complex network model based on time influence domain, i.e.…”

Section: Introductionmentioning

confidence: 99%

Using complex network theory for temporal locality in network traffic flows

Wang

et al. 2019

Physica A: Statistical Mechanics and its Applications

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Monitoring the interaction behaviors of network traffic flows and detecting unwanted Internet applications and anomalous flows have become a challenging problem, since many applications obfuscate their network traffic flow using unregistered port numbers or payload encryption. In this paper, the temporal locality complex network model-TLCN is proposed as a way to monitor, analyze and visualize network traffic flows. TLCNs model the interaction behaviors of large-scale network traffic flows, where the nodes and the edges can be defined to represent different flow levels and flow interactions separately. Then, the statistical characteristics and dynamic behaviors of the TLCNs are studied to represent TLCN's structure representing ability to the flow interactions. According to the analysis of TLCN statistical characteristics with different Internet applications, we found that the weak interaction flows prefer to form the small-world TLCN and the strong interaction flows prefer to the scale-free TLCN. In the studies of anomaly behaviors of TLCNs, the network structure of attacked TLCNs can have a remarkable feature for three attack patterns, and the evolution of TLCNs exhibits a good consistency between TLCN structure and attack process. With the introduction of TLCNs, we are able to harness a wealth of tools and graph modeling techniques from a diverse set of disciplines.

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“…Through analysing the structural properties and topological parameters of the complex network, dynamic information and inherent laws of the hydrological regime hidden in the time series can be explored via the topological statistics [36][37][38]. Therefore, the complex network model has been widely used in time series analysis, and great progress has been made in studies analysing stock holdings [39], tourist flows [36], natural disasters [40], stock markets [37,41], crude oil prices, and trade [25,42,43]. However, this method is seldom used in the field of hydrology, let alone in analysing the differences of hydrological regimes before and after the construction of human projects.…”

Section: Introductionmentioning

confidence: 99%

Using a Complex Network to Analyze the Effects of the Three Gorges Dam on Water Level Fluctuation in Poyang Lake

Ning

Zhou

Cheng

et al. 2019

IJGI

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Because the Three Gorges Dam (TGD) has disturbed the normal hydrological regime downstream, analyzing the influence of the TGD on water level fluctuation is of great importance to ecological planning. The distribution and dynamic of the water level before and after the TGD were analyzed using frequency distribution and a complex network. Frequency distribution was unimodal before the TGD, and the peak ranged from 13-15 m. Frequency distribution was bimodal after TGD and two peaks ranged from 9-10 m and 16-17 m. The number of days when the water level was above warning level was reduced, and it was increased when the water level was below the ecological level. Further, the TGD had little effect on the number of days of rapid water level rising, which mainly existed during the flood season. However, this imposed a greater influence on the number of days of rapid water level decline, which implies a weaker intensity of the recession process, along with a longer duration. Thirdly, in winter and spring, the water level after the TGD was lower than that before the TGD by approximately 1 m. In summer, the number of days when the water level was above warning level was reduced. In autumn, the frequency distribution changed from unimodal to bimodal. The TGD has the greatest influence during the winter, which resulted in a lower water level and more severe drought.

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From time series to complex networks: The phase space coarse graining

Cited by 78 publications

References 40 publications

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

Using complex network theory for temporal locality in network traffic flows

Using a Complex Network to Analyze the Effects of the Three Gorges Dam on Water Level Fluctuation in Poyang Lake

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