The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Jurgen Kurths - One of the best experts on this subject based on the ideXlab platform.
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complex network approaches to nonlinear Time Series Analysis
Physics Reports, 2019Co-Authors: Yong Zou, Reik V Donner, Norbert Marwan, Jonathan F Donges, Jurgen KurthsAbstract:Abstract In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on Time Series. While both nonlinear Time Series Analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear Time Series Analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of Time Series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear Time Series Analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear Time Series Analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of Time Series networks for tackling real-world contemporary scientific problems. The overall aim of this report is to provide the readers with the knowledge how the complex network approaches can be applied to their own field of real-world Time Series Analysis.
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recurrence based Time Series Analysis by means of complex network methods
International Journal of Bifurcation and Chaos, 2011Co-Authors: Reik V Donner, Yong Zou, Norbert Marwan, Jonathan F Donges, Jurgen Kurths, Michael Small, Ruoxi XiangAbstract:Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the Analysis of dynamically relevant higher-order statistical properties of Time Series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in Time Series Analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world Time Series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of Time Series an...
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recurrence based Time Series Analysis by means of complex network methods
arXiv: Chaotic Dynamics, 2010Co-Authors: Reik V Donner, Yong Zou, Norbert Marwan, Jonathan F Donges, Jurgen Kurths, Michael Small, Ruoxi XiangAbstract:Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the Analysis of dynamically relevant higher-order statistical properties of Time Series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in Time Series Analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world Time Series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of Time Series Analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.
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recurrence networks a novel paradigm for nonlinear Time Series Analysis
New Journal of Physics, 2010Co-Authors: Reik V Donner, Yong Zou, Norbert Marwan, Jonathan F Donges, Jurgen KurthsAbstract:This paper presents a new approach for analysing the structural properties of Time Series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a Time Series is interpreted as the adjacency matrix of an associated complex network, which links different points in Time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming Time Series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a Time Series, most of which are not yet provided by other existing methods of nonlinear Time Series Analysis.
Eleonora Papadimitriou - One of the best experts on this subject based on the ideXlab platform.
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on statistical inference in Time Series Analysis of the evolution of road safety
Accident Analysis & Prevention, 2013Co-Authors: Jacques J F Commandeur, Frits Bijleveld, Ruth Bergelhayat, Constantinos Antoniou, George Yannis, Eleonora PapadimitriouAbstract:Data collected for building a road safety observatory usually include observations made sequentially through Time. Examples of such data, called Time Series data, include annual (or monthly) number of road traffic accidents, traffic fatalities or vehicle kilometers driven in a country, as well as the corresponding values of safety performance indicators (e.g., data on speeding, seat belt use, alcohol use, etc.). Some commonly used statistical techniques imply assumptions that are often violated by the special properties of Time Series data, namely serial dependency among disturbances associated with the observations. The first objective of this paper is to demonstrate the impact of such violations to the applicability of standard methods of statistical inference, which leads to an under or overestimation of the standard error and consequently may produce erroneous inferences. Moreover, having established the adverse consequences of ignoring serial dependency issues, the paper aims to describe rigorous statistical techniques used to overcome them. In particular, appropriate Time Series Analysis techniques of varying complexity are employed to describe the development over Time, relating the accident-occurrences to explanatory factors such as exposure measures or safety performance indicators, and forecasting the development into the near future. Traditional regression models (whether they are linear, generalized linear or nonlinear) are shown not to naturally capture the inherent dependencies in Time Series data. Dedicated Time Series Analysis techniques, such as the ARMA-type and DRAG approaches are discussed next, followed by structural Time Series models, which are a subclass of state space methods. The paper concludes with general recommendations and practice guidelines for the use of Time Series models in road safety research.
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On statistical inference in Time Series Analysis of the evolution of road safety
Accident Analysis and Prevention, 2013Co-Authors: Jjf Commandeur, Frits Bijleveld, Constantinos Antoniou, George Yannis, Ruth Bergel Hayat, Eleonora PapadimitriouAbstract:Data collected for building a road safety observatory usually include observations made sequentially through Time. Examples of such data, called Time Series data, include annual (or monthly) number of road traffic accidents, traffic fatalities or vehicle kilometers driven in a country, as well as the corresponding values of safety performance indicators (e.g., data on speeding, seat belt use, alcohol use, etc.). Some commonly used statistical techniques imply assumptions that are often violated by the special properties of Time Series data, namely serial dependency among disturbances associated with the observations. The first objective of this paper is to demonstrate the impact of such violations to the applicability of standard methods of statistical inference, which leads to an under or overestimation of the standard error and consequently may produce erroneous inferences. Moreover, having established the adverse consequences of ignoring serial dependency issues, the paper aims to describe rigorous statistical techniques used to overcome them. In particular, appropriate Time Series Analysis techniques of varying complexity are employed to describe the development over Time, relating the accident-occurrences to explanatory factors such as exposure measures or safety performance indicators, and forecasting the development into the near future. Traditional regression models (whether they are linear, generalized linear or nonlinear) are shown not to naturally capture the inherent dependencies in Time Series data. Dedicated Time Series Analysis techniques, such as the ARMA-type and DRAG approaches are discussed next, followed by structural Time Series models, which are a subclass of state space methods. The paper concludes with general recommendations and practice guidelines for the use of Time Series models in road safety research.
Venkatesh Rajagopalan - One of the best experts on this subject based on the ideXlab platform.
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symbolic Time Series Analysis via wavelet based partitioning
Signal Processing, 2006Co-Authors: Venkatesh RajagopalanAbstract:Symbolic Time Series Analysis (STSA) of complex systems for anomaly detection has been recently introduced in literature. An important feature of the STSA method is extraction of relevant information, imbedded in the measured Time Series data, to generate symbol sequences. This paper presents a wavelet-based partitioning approach for symbol generation, instead of the currently practiced method of phase-space partitioning. Various aspects of the proposed technique, such as wavelet selection, noise mitigation, and robustness to spurious disturbances, are discussed. The wavelet-based partitioning in STSA is experimentally validated on laboratory apparatuses for anomaly/damage detection. Its efficacy is investigated by comparison with phase-space partitioning.
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symbolic Time Series Analysis for anomaly detection a comparative evaluation
Signal Processing, 2005Co-Authors: Shin C Chin, Asok Ray, Venkatesh RajagopalanAbstract:Recent literature has reported a novel method for anomaly detection in complex dynamical systems, which relies on symbolic Time Series Analysis and is built upon the principles of automata theory and pattern recognition. This paper compares the performance of this symbolic-dynamics-based method with that of other existing pattern recognition techniques from the perspectives of early detection of small anomalies. Time Series data of observed process variables on the fast Time-scale of dynamical systems are analyzed at slow Time-scale epochs of (possible) anomalies. The results are derived from experiments on a nonlinear electronic system with a slowly varying dissipation parameter.
Jonathan F Donges - One of the best experts on this subject based on the ideXlab platform.
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complex network approaches to nonlinear Time Series Analysis
Physics Reports, 2019Co-Authors: Yong Zou, Reik V Donner, Norbert Marwan, Jonathan F Donges, Jurgen KurthsAbstract:Abstract In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on Time Series. While both nonlinear Time Series Analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear Time Series Analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of Time Series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear Time Series Analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear Time Series Analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of Time Series networks for tackling real-world contemporary scientific problems. The overall aim of this report is to provide the readers with the knowledge how the complex network approaches can be applied to their own field of real-world Time Series Analysis.
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recurrence based Time Series Analysis by means of complex network methods
International Journal of Bifurcation and Chaos, 2011Co-Authors: Reik V Donner, Yong Zou, Norbert Marwan, Jonathan F Donges, Jurgen Kurths, Michael Small, Ruoxi XiangAbstract:Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the Analysis of dynamically relevant higher-order statistical properties of Time Series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in Time Series Analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world Time Series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of Time Series an...
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recurrence based Time Series Analysis by means of complex network methods
arXiv: Chaotic Dynamics, 2010Co-Authors: Reik V Donner, Yong Zou, Norbert Marwan, Jonathan F Donges, Jurgen Kurths, Michael Small, Ruoxi XiangAbstract:Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the Analysis of dynamically relevant higher-order statistical properties of Time Series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in Time Series Analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world Time Series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of Time Series Analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.
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recurrence networks a novel paradigm for nonlinear Time Series Analysis
New Journal of Physics, 2010Co-Authors: Reik V Donner, Yong Zou, Norbert Marwan, Jonathan F Donges, Jurgen KurthsAbstract:This paper presents a new approach for analysing the structural properties of Time Series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a Time Series is interpreted as the adjacency matrix of an associated complex network, which links different points in Time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming Time Series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a Time Series, most of which are not yet provided by other existing methods of nonlinear Time Series Analysis.
Asok Ray - One of the best experts on this subject based on the ideXlab platform.
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space partitioning via hilbert transform for symbolic Time Series Analysis
Applied Physics Letters, 2008Co-Authors: Aparna Subbu, Asok RayAbstract:Symbol sequence generation is a crucial step in symbolic Time Series Analysis of dynamical systems, which requires phase-space partitioning. This letter presents analytic signal space partitioning (ASSP) that relies on Hilbert transform of the observed real-valued data sequence into the corresponding complex-valued analytic signal. ASSP yields comparable performance as other partitioning methods, such as symbolic false nearest neighbor partitioning (SFNNP) and wavelet-space partitioning (WSP). The execution Time of ASSP is several orders of magnitude smaller than that of SFNNP. Compared to WSP, the ASSP algorithm is analytically more rigorous and is approximately five Times faster.
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symbolic Time Series Analysis for anomaly detection a comparative evaluation
Signal Processing, 2005Co-Authors: Shin C Chin, Asok Ray, Venkatesh RajagopalanAbstract:Recent literature has reported a novel method for anomaly detection in complex dynamical systems, which relies on symbolic Time Series Analysis and is built upon the principles of automata theory and pattern recognition. This paper compares the performance of this symbolic-dynamics-based method with that of other existing pattern recognition techniques from the perspectives of early detection of small anomalies. Time Series data of observed process variables on the fast Time-scale of dynamical systems are analyzed at slow Time-scale epochs of (possible) anomalies. The results are derived from experiments on a nonlinear electronic system with a slowly varying dissipation parameter.
