Visibility graph analysis for re-sampled time series from auto-regressive stochastic processes

Zhang, Rong; Zou, Yong; Zhou, Jie; Gao, Zhong-Ke; Guan, Shuguang

doi:10.1016/j.cnsns.2016.04.031

Cited by 29 publications

(21 citation statements)

References 35 publications

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“…It follows that, for uncorrelated random series, the associated average degree is (Nuñez, Lacasa, Valero, Gómez, & Luque, 2012):

\overset{k}{true} = \sum italickP ((), k) = \sum_{k = 2}^{\infty} \frac{k}{3} {(\frac{2}{3})}^{k - 2} = 4 .

Additionally, Lacasa and Toral (2010) suggested that the degree distribution follows the exponential law, P ( k ) ∼ exp (− λk ) , where the value of λ depends on the type of process generating the time series:

λ < \ln ((), \frac{3}{2})

for chaotic processes,

λ > \ln ((), \frac{3}{2})

for stochastic processes and

λ = \ln ((), \frac{3}{2})

for uncorrelated processes. However, note that Ravetti, Carpi, Gonçalves, Frery, and Rosso (2014) found that for the Rössler system 6 the rule is not valid, and Zhang, Zou, Zhou, Gao, and Guan (2017) found results in which negatively correlated processes lead to lower λ values than the critical value. These results show that there are exceptions to the rule and that using λ to distinguish chaotic from stochastic processes requires further investigation.…”

Section: Mapping Univariate Time Series Into Complex Networkmentioning

confidence: 99%

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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“…It follows that, for uncorrelated random series, the associated average degree is (Nuñez, Lacasa, Valero, Gómez, & Luque, 2012):

\overset{k}{true} = \sum italickP ((), k) = \sum_{k = 2}^{\infty} \frac{k}{3} {(\frac{2}{3})}^{k - 2} = 4 .

λ < \ln ((), \frac{3}{2})

for chaotic processes,

λ > \ln ((), \frac{3}{2})

for stochastic processes and

λ = \ln ((), \frac{3}{2})

Section: Mapping Univariate Time Series Into Complex Networkmentioning

confidence: 99%

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

“…It has a wide application in various fields, such as linguistics and computer science. Especially, many pieces of researches about complex networks apply some advanced knowledge of graph theory [52], [53].…”

Section: A Graph Theorymentioning

confidence: 99%

An Efficient Network Method for Time Series Forecasting Based on the DC Algorithm and Visibility Relation

Zhao

Mo²,

Deng

2020

IEEE Access

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Recently time series prediction based on network analysis has become a hot research topic. However, how to more accurately forecast time series with good efficiency is still an open question. To address this issue, we propose an efficient time series forecasting method based on the DC algorithm and visibility relations on the vertexes set. Firstly, the time series is mapped into the network by the DC algorithm, which is a more efficient approach to generate the visibility graph. Then, we use the variation trends (slope) of those nodes that have visibility relation with the last node to get the preliminary predictive values. Afterward, the value of the last node is adopted to obtain the revised predictive values, which are assigned different weights according to node degree and time distance to get the final weighted result. To better demonstrate the prediction performance and applicability of the proposed method, the proposed method is applied to different time series data sets. The empirical results show that the proposed method could provide a higher level of forecasting accuracy than many methods with relatively lower time complexity. INDEX TERMS Complex network, time series forecasting, node degree, visibility graph, variation trend.

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“…对于非关联噪声, 水平可视图p(k) ∼ e −λk , 尤其当白噪声时, λ c = ln(3/2) [76,79] . 但是运用临界指数λ c 来区分随机过程和混沌系统时, 必须小心验证其可靠性 [80,81] .…”

Section: 可视图基本性质unclassified