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

Wang, Minggang; Vilela, André L. M.; Du, Ruxu; Zhao, Longfeng; Dong, Gaogao; Li, Tian; Stanley, H. Eugene

doi:10.1038/s41598-018-23388-1

Cited by 26 publications

(21 citation statements)

References 46 publications

(95 reference statements)

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“…Wang et al (2018) presents some exact results (similar to those obtained for the HVGs presented in Section 3.1.2) on the topological properties of the LPHVG associated with bi‐infinite time series of i.i.d. random variables with a probability density f ( x ).…”

Section: Mapping Univariate Time Series Into Complex Networksupporting

confidence: 53%

“…From Equation () we obtain the average degree

\overset{k}{true}

\overset{k}{true} = \sum italickP ((), k) = 4 ((), l + 1) .

And based on the Equation ) we can deduce the minimum and maximum local clustering coefficient of the LPHVG associated to i.i.d. random series as (see Wang, Vilela, et al, 2018 for more details):

C_{\min} ((), k) = \frac{2}{k} + \frac{2 l ((), k - 2)}{k ((), k - 1)}, l = 0,1,2, \dots; k \geq 2 ((), l + 1)

C_{\max} ((), k) = \frac{2}{k} + \frac{4 l ((), k - 3)}{k ((), k - 1)}, l = 0,1,2, \dots; k \geq 2 ((), 2 l + 1) .

For an infinite periodic series of period P the average degree depends on the period P :

\overset{k}{true} = 4 ((), l + 1) ((), 1 - \frac{2 l + 1}{2 P}), l ≪ P .

LPHVG was employed in the analysis of EEG signals and biphasic‐flow signals where they characterize the behaviors underlying the systems (Gao, Cai, et al, 2016), in the analysis of chaotic series and energy and oil price series (Wang, Vilela, et al, 2018), and to distinguish between random, periodic and chaotic signals using motifs (Wang, Xu, et al, 2018).…”

Section: Mapping Univariate Time Series Into Complex Networkmentioning

confidence: 99%

“…And based on the Equation ( 12) we can deduce the minimum and maximum local clustering coefficient of the LPHVG associated to i.i.d. random series as (see Wang, Vilela, et al, 2018 for more details): For an infinite periodic series of period P the average degree depends on the period P:…”

Section: Limited Penetrable Visibility Graphsmentioning

confidence: 99%

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Time series analysis via network science: Concepts and algorithms

Silva

Ribeiro

et al. 2021

WIREs Data Min & Knowl

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There is nowadays a constant flux of data being generated and collected in all types of real world systems. These data sets are often indexed by time, space, or both requiring appropriate approaches to analyze the data. In univariate settings, time series analysis is a mature field. However, in multivariate contexts, time series analysis still presents many limitations. In order to address these issues, the last decade has brought approaches based on network science. These methods involve transforming an initial time series data set into one or more networks, which can be analyzed in depth to provide insight into the original time series. This review provides a comprehensive overview of existing mapping methods for transforming time series into networks for a wide audience of researchers and practitioners in machine learning, data mining, and time series. Our main contribution is a structured review of existing methodologies, identifying their main characteristics, and their differences. We describe the main conceptual approaches, provide authoritative references and give insight into their advantages and limitations in a unified way and language. We first describe the case of univariate time series, which can be mapped to single layer networks, and we divide the current mappings based on the underlying concept: visibility, transition, and proximity. We then proceed with multivariate time series discussing both single layer and multiple layer approaches. Although still very recent, this research area has much potential and with this survey we intend to pave the way for future research on the topic. This article is categorized under: Fundamental Concepts of Data and Knowledge > Data Concepts Fundamental Concepts of Data and Knowledge > Knowledge Representation

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Section: Mapping Univariate Time Series Into Complex Networksupporting

confidence: 53%

“…From Equation () we obtain the average degree

\overset{k}{true}

\overset{k}{true} = \sum italickP ((), k) = 4 ((), l + 1) .

And based on the Equation ) we can deduce the minimum and maximum local clustering coefficient of the LPHVG associated to i.i.d. random series as (see Wang, Vilela, et al, 2018 for more details):

C_{\min} ((), k) = \frac{2}{k} + \frac{2 l ((), k - 2)}{k ((), k - 1)}, l = 0,1,2, \dots; k \geq 2 ((), l + 1)

C_{\max} ((), k) = \frac{2}{k} + \frac{4 l ((), k - 3)}{k ((), k - 1)}, l = 0,1,2, \dots; k \geq 2 ((), 2 l + 1) .

For an infinite periodic series of period P the average degree depends on the period P :

\overset{k}{true} = 4 ((), l + 1) ((), 1 - \frac{2 l + 1}{2 P}), l ≪ P .

Section: Mapping Univariate Time Series Into Complex Networkmentioning

confidence: 99%

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Time series analysis via network science: Concepts and algorithms

Silva

Ribeiro

et al. 2021

WIREs Data Min & Knowl

View full text Add to dashboard Cite

show abstract

“…This bridge between time series, dynamic systems, and graph theory allows, with relative ease, the inference of a system’s features that would have been derivable with much more complex techniques (nonlinear analyses) and, in certain conditions, the highlighting of features that other methods are not fully able to emphasize, such as changes in the dynamic behavior of the system (e.g., Baggio and Sainaghi 2011). This methodology has had many applications in different domains (M. Wang et al 2018) including tourism (Baggio and Sainaghi 2016; Sainaghi and Baggio 2014, 2017).…”

Section: Literature Reviewmentioning

confidence: 99%

Destination Events, Stability, and Turning Points of Development

Sainaghi

Baggio

2019

Journal of Travel Research

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This study investigates the effects generated by tourism events and investments to improve destination development (dynamics) and stability (topology). The horizontal visibility graph framework (a technique able to transform a time series into a network) was used. Two hypotheses were tested: the first was the ability of these events and investments to generate a turning point, and the second was their ability to increase the system’s stability. The findings are based on a longitudinal analysis of three different destinations in terms of size, type of destination events and investments, and the prevalent market segment. For each case, a daily longitudinal time series was considered, and the empirical evidence confirmed both hypotheses. In the concluding remarks, the theoretical and empirical implications are reported, and some future research avenues are discussed.

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“…e method's primary thought is to express the complex system using complex network and then reveal the essential characteristics of the system by using the network topology. In this field, a series of algorithms have been developed to convert the nonlinear time series of a single variable into a complex network, such as visibility methods, including natural visibility graph [12], horizontal visibility graph [13], parametric natural visibility graph [14], limited penetrable horizontal visibility graph [15], and parametric modified limited penetrable visibility graph [16], the mapping algorithm for pseudoperiodic time series [17], phase space roughening algorithm [18], and algorithms based on phase space reconstruction [19,20]. For multivariate time series, scholars have carried out a significant amount of research on how to analyze multivariate time series using complex networks.…”

Section: Introductionmentioning

confidence: 99%

Information Linkage between Carbon and Energy Markets: Multiplex Recurrence Network Approach

Wang

Yang

2020

Complexity

Self Cite

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In this paper, a multilayer recurrence network is introduced to examine the information linkage between carbon and energy markets. We first construct a multilayer recurrence network of energy and carbon markets, and we define the information linkage coefficient to measure the linkage relationship between the network layers based on the network microstructure. To measure the mutual leading relationship between carbon and energy markets, we construct a time-delay multilayer recurrence network and introduce the time-delay information linkage coefficient to measure the intersystem interaction. The carbon and energy prices, including West Texas Intermediate crude oil, coal, natural gas, and gasoline, from February 22, 2011, to April 1, 2019, are selected as sample data for empirical analysis. The results show that the linkage relationship between oil, coal, natural gas, and carbon prices presents a U-shaped trend in the second, transitional, and third phases of the European Union carbon market, while the linkage trend of gasoline and carbon prices continues to rise. The mutual leading relationship between energy and carbon prices changes in different stages, and carbon price plays a leading role at the present stage.

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

Cited by 26 publications

References 46 publications

Time series analysis via network science: Concepts and algorithms

Time series analysis via network science: Concepts and algorithms

Destination Events, Stability, and Turning Points of Development

Information Linkage between Carbon and Energy Markets: Multiplex Recurrence Network Approach

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