Pattern interdependent network of cross-correlation in multivariate time series

Ren, Henggang; Yuan, Qianshun; Semba, Sherehe; Weng, Tongfeng; Gu, Changgui

doi:10.1016/j.physleta.2020.126781

Cited by 9 publications

(4 citation statements)

References 46 publications

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“…Based on the visibility graphlets networks (Section 3.2.4) recently, Ren et al (2020) proposed the pattern interdependent networks to represent the cross‐correlation patterns in a stationary bivariate time series,

{\{Y_{i, t}\}}_{i = 1}^{2}

. The method consists in generating the state chain network (following the algorithm presented in Section 3.2.4) for each time series component, resulting in a bi‐graphlet series:

((), \begin{array}{c} G_{1}^{[1]} \to G_{2}^{[1]} \to \dots \to G_{T - w + 1}^{[1]} \\ G_{1}^{[2]} \to G_{2}^{[2]} \to \dots \to G_{T - w + 1}^{[2]} \end{array}) .

Similar to visibility graphlets networks, all unique graphlets G i are identified.…”

Section: Mapping Multivariate Time Series Into Complex Networkmentioning

confidence: 99%

“…Ren et al (2020) applied this method to synthetic bivariate time series and showed that a set of unique graphlets and the topological structure of the resulting networks is determined and dependent on the cross‐correlation, and that the differences in features, such as Hurst exponent, of the time series components determine the symmetry of the edges of the network.…”

Section: Mapping Multivariate 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

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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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{\{Y_{i, t}\}}_{i = 1}^{2}

. The method consists in generating the state chain network (following the algorithm presented in Section 3.2.4) for each time series component, resulting in a bi‐graphlet series:

((), \begin{array}{c} G_{1}^{[1]} \to G_{2}^{[1]} \to \dots \to G_{T - w + 1}^{[1]} \\ G_{1}^{[2]} \to G_{2}^{[2]} \to \dots \to G_{T - w + 1}^{[2]} \end{array}) .

Similar to visibility graphlets networks, all unique graphlets G i are identified.…”

Section: Mapping Multivariate Time Series Into Complex Networkmentioning

confidence: 99%

Section: Mapping Multivariate 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

“…(iv) Graph-lets Let a window with a specified length w slide along the EV/EI series, the visibility graphs for the covered series segments are called graph-lets, representing the states of the system in the corresponding time durations. [34][35][36][37][38][39][40][41][42][43] The successive graph-lets gives us the evolutionary trajectory 100505-3 of the system. One enumerates all the possible distinguishable graph-lets and give them each identification numbers such as 1, 2, .…”

Section: Network Propertiesmentioning

confidence: 99%

Visibility graph approach to extreme event series

Zhang 张,

Chen 陈,

Wang 王

et al. 2023

Chinese Phys. B

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An extreme event may lead to serious disaster to a complex system. In an extreme event series there exist generally non-trivial patterns covering different time scales. Investigations on extreme events are currently based upon statistics, where the patterns are merged into averages. In this paper from extreme the event series we constructed extreme value series and extreme interval series. And the visibility graph is then adopted to display the patterns formed by the increases/decreases of extreme value or interval faster/slower than the linear ones. For the fractional Brownian motions, the properties for the constructed networks are the persistence, threshold, and event-type independent, e.g., the degree distributions decay exponentially with almost identical speeds, the nodes cluster into modular structures with large and similar modularity degrees, and each specific network has a perfect hierarchical structure. For the volatilities of four stock markets (NSDQ, SZI, FTSE100, and HSI), the properties for the former three’s networks are the threshold and market independent. Comparing with the factional Brownian motions, their degree distributions decay exponentially but with slower speeds, their modularity behaviors are significant but with smaller modularity degrees. The fourth market behave similar qualitatively but different quantitatively with the three markets. Interestingly, all the transition frequency networks share an identical backbone composed of nine edges and the linked graphlets. The universal behaviors give us a framework to describe extreme events from the viewpoint of network.

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“…Recent developments have introduced the concept of an ordinal network based on pattern co-occurrence between time series [28]. This approach facilitates the inference of correlations between different time series.…”

Section: Introductionmentioning

confidence: 99%

Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods

Almendral

Leyva

Sendiña‐Nadal

2023

Entropy

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Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand information interchange in the networks of dynamical systems, and uncover the interplay between dynamics and structure during the synchronization process, remains relatively unexplored. Here, we compare the ordinal permutation entropy, a standard complexity measure in the literature, and the permutation entropy of the ordinal transition probability matrix that describes the transitions between the ordinal patterns derived from a time series. We find that the permutation entropy based on the ordinal transition matrix outperforms the rest of the tested measures in discriminating the topological role of networked chaotic Rössler systems. Since the method is based on permutation entropy measures, it can be applied to arbitrary real-world time series exhibiting correlations originating from an existing underlying unknown network structure. In particular, we show the effectiveness of our method using experimental datasets of networks of nonlinear oscillators.

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Pattern interdependent network of cross-correlation in multivariate time series

Cited by 9 publications

References 46 publications

Time series analysis via network science: Concepts and algorithms

Time series analysis via network science: Concepts and algorithms

Visibility graph approach to extreme event series

Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods

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