Characterization of dynamical systems under noise using recurrence networks: Application to simulated and EEG data

Subramaniyam, Narayan Puthanmadam; Hyttinen, Jari

doi:10.1016/j.physleta.2014.10.005

Cited by 32 publications

(13 citation statements)

References 47 publications

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“…[31]). These findings have been confirmed by another study, reporting an increasing degree of structural complexity in the EEG of normal subjects compared to the EEG from epilepsy patients [32].…”

Section: Introductionsupporting

confidence: 65%

Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data

et al. 2016

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We investigate the suitability of selected measures of complexity based on recurrence quantification analysis and recurrence networks for an identification of pre-seizure states in multi-day, multi-channel, invasive electroencephalographic recordings from five epilepsy patients. We employ several statistical techniques to avoid spurious findings due to various influencing factors and due to multiple comparisons and observe precursory structures in three patients. Our findings indicate a high congruence among measures in identifying seizure precursors and emphasize the current notion of seizure generation in large-scale epileptic networks. A final judgment of the suitability for field studies, however, requires evaluation on a larger database.

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Section: Introductionsupporting

confidence: 65%

Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data

et al. 2016

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“…Particularly, the values of average clustering coefficient C and the average path length L are high for dynamical systems exhibiting periodic dynamics compared to chaotic dynamics. Recently, it was also shown that, after embedding, the recurrence networks constructed from the surrogates, which are Gaussian, linear stochastic processes, exhibit lower values of average clustering coefficient and average path length compared to the original data that have some deterministic (chaotic) dynamics [33]. Hence, comparing the topological characteristics of the complex networks generated from surrogate time series with that of the original EEG signal yields an interesting way to study the presence of any existing nonrandom structure in the original EEG time series [33].…”

Section: Impact Of Nonstationaritymentioning

confidence: 99%

“…Recently, it was also shown that, after embedding, the recurrence networks constructed from the surrogates, which are Gaussian, linear stochastic processes, exhibit lower values of average clustering coefficient and average path length compared to the original data that have some deterministic (chaotic) dynamics [33]. Hence, comparing the topological characteristics of the complex networks generated from surrogate time series with that of the original EEG signal yields an interesting way to study the presence of any existing nonrandom structure in the original EEG time series [33]. Our results indicate that the complex networks obtained from the focal EEG signals are more assortative and clustered compared to that of the complex networks obtained from the nonfocal EEG signals, which possibly have more random structure in them.…”

Section: Impact Of Nonstationaritymentioning

confidence: 99%

“…Recurrence network measures like the average clustering coefficient C and average path length L have been used to compare the dynamical properties of EEG signals derived from healthy and epileptic patients [32,33]. Particularly, bivariate measures derived from cross-recurrence networks have not been investigated to identify interdependence between two EEG time series.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Subramaniyam

Hyttinen

2015

Phys. Rev. E

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Recently Andrezejak et al. combined the randomness and nonlinear independence test with iterative amplitude adjusted Fourier transform (iAAFT) surrogates to distinguish between the dynamics of seizure-free intracranial electroencephalographic (EEG) signals recorded from epileptogenic (focal) and nonepileptogenic (nonfocal) brain areas of epileptic patients. However, stationarity is a part of the null hypothesis for iAAFT surrogates and thus nonstationarity can violate the null hypothesis. In this work we first propose the application of the randomness and nonlinear independence test based on recurrence network measures to distinguish between the dynamics of focal and nonfocal EEG signals. Furthermore, we combine these tests with both iAAFT and truncated Fourier transform (TFT) surrogate methods, which also preserves the nonstationarity of the original data in the surrogates along with its linear structure. Our results indicate that focal EEG signals exhibit an increased degree of structural complexity and interdependency compared to nonfocal EEG signals. In general, we find higher rejections for randomness and nonlinear independence tests for focal EEG signals compared to nonfocal EEG signals. In particular, the univariate recurrence network measures, the average clustering coefficient C and assortativity R, and the bivariate recurrence network measure, the average cross-clustering coefficient C(cross), can successfully distinguish between the focal and nonfocal EEG signals, even when the analysis is restricted to nonstationary signals, irrespective of the type of surrogates used. On the other hand, we find that the univariate recurrence network measures, the average path length L, and the average betweenness centrality BC fail to distinguish between the focal and nonfocal EEG signals when iAAFT surrogates are used. However, these two measures can distinguish between focal and nonfocal EEG signals when TFT surrogates are used for nonstationary signals. We also report an improvement in the performance of nonlinear prediction error N and nonlinear interdependence measure L used by Andrezejak et al., when TFT surrogates are used for nonstationary EEG signals. We also find that the outcome of the nonlinear independence test based on the average cross-clustering coefficient C(cross) is independent of the outcome of the randomness test based on the average clustering coefficient C. Thus, the univariate and bivariate recurrence network measures provide independent information regarding the dynamics of the focal and nonfocal EEG signals. In conclusion, recurrence network analysis combined with nonstationary surrogates can be applied to derive reliable biomarkers to distinguish between epileptogenic and nonepileptogenic brain areas using EEG signals.

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“…The underlying principle in this approach is to characterize the topology of the resultant network using tools from graph theory to gain insights into the dynamics underlying the time series. Complex network-based univariate and multivariate time-series analysis has been successfully applied in different fields, including climatology [1,15,22] fluid dynamics [23][24][25][26] and neuroscience [27][28][29][30], to cite a few.…”

Section: Introductionmentioning

confidence: 99%

Signatures of chaotic and stochastic dynamics uncovered with ε -recurrence networks

2015

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An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, ε -recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global ε -recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rössler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global ε -recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high noise levels and short data lengths. Furthermore, ε -recurrence network analysis of the real-world epileptic data revealed the capability of these network measures in capturing dynamical transitions using short window sizes. ε -recurrence network analysis is a powerful method in uncovering the signatures of chaotic and stochastic dynamics based on the geometrical properties of time series.

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Characterization of dynamical systems under noise using recurrence networks: Application to simulated and EEG data

Cited by 32 publications

References 47 publications

Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data

Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Signatures of chaotic and stochastic dynamics uncovered with ε -recurrence networks

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