Directed vector visibility graph from multivariate time series: a new method to measure time series irreversibility

Shang, Binbin; Shang, Pengjian

doi:10.1007/s11071-021-06340-3

Cited by 7 publications

(2 citation statements)

References 49 publications

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“…The Visibility Graph approach presented in Section 2.7 has been modified by several authors. Some proposals include the use of an asynchronicity metric to compare the sequences of degrees of nodes, in the forward and backward time series [112]; the use of permutation patterns to encode node degrees [113]; the use of higher moments [114] and singular value decomposition [115] to analyse the node degree sequence; the analysis of motifs [116]; and ways to encode multivariate time series in the visibility graph [117].…”

Section: Additional Irreversibility Testsmentioning

confidence: 99%

Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison

Zanin

Papo

2021

Entropy

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The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.

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Section: Additional Irreversibility Testsmentioning

confidence: 99%

Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison

Zanin

Papo

2021

Entropy

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“…Other types of visibility graphs [ 61 ] have been proposed to obtain the network with different structure based on the feature of time series, such as (un-) weighted, (un-) directed, and (single-) multi-layered networks. Numerous properties in the time series can be revealed by the family of visibility graphs, for example, estimating the Hurst exponent of fractal stochastic processes [ 62 , 63 ], proving the relationship between the power-law degree distribution and fractality in series [ 57 ], analyzing multifractal properties of time series [ 64 ], and measuring the irreversibility of real-valued time series [ 65 – 67 ]. In addition, it has been applied in different fields to address practical problems, including studying the dynamics of a passive scalar plume [ 68 ], planning long-voyage routes [ 69 ], analyzing electroencephalogram signals [ 70 ], extracting hidden information in coupled timessss series [ 71 , 72 ], and aggregating data in complex systems [ 73 ].…”

Section: Introductionmentioning

confidence: 99%

Visibility graph for time series prediction and image classification: a review

2022

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The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

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