Testing for nonlinearity in irregular fluctuations with long-term trends

Nakamura, Tomomichi; Small, Michael; Hirata, Yoshito

doi:10.1103/physreve.74.026205

Cited by 41 publications

(72 citation statements)

References 20 publications

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“…,N/2) of the N -point Fourier transformed data, where N is the number of points in the data. This way, local nonstationarity and even global nonstationarity, i.e., trends (for sufficiently high f c ), are preserved in the generated surrogates [36] but at the same time local structures in short-term variability are destroyed [35]. As iis evident, generation of TFT surrogates crucially depends on the choice of cutoff frequency f c , which is the maximum preserved frequency.…”

Section: Tft Surrogatesmentioning

confidence: 96%

“…[5]. In order to make the results more reliable, particularly in the case of nonstationary EEG signals, we also use the truncated Fourier transform (TFT) surrogates proposed by Nakamura et al [35]. TFT surrogates are particularly useful in preserving some nonstationarity present in the original data in the surrogates, unlike the iAAFT surrogates which can only preserve the linear properties [35,36].…”

Section: Introductionmentioning

confidence: 99%

“…In order to make the results more reliable, particularly in the case of nonstationary EEG signals, we also use the truncated Fourier transform (TFT) surrogates proposed by Nakamura et al [35]. TFT surrogates are particularly useful in preserving some nonstationarity present in the original data in the surrogates, unlike the iAAFT surrogates which can only preserve the linear properties [35,36]. Particularly, we test for randomness based on network measures, the average clustering coefficient C, assortativity R, the average path length L, and the average betweenness centrality BC and independence based on crossnetwork measure, the average cross-clustering coefficient C cross in the focal and nonfocal EEG signals.…”

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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Section: Tft Surrogatesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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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“…In the field of nonlinear time series analysis, many different surrogate algorithms [31][32][33][34] have been proposed. Each of these algorithms is used to provide a robust statistical test of some specified null hypotheses.…”

Section: Surrogatesmentioning

confidence: 99%

Dynamical Systems Induced on Networks Constructed from Time Series

Hou

Small

Lao

2015

Entropy

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Several methods exist to construct complex networks from time series. In general, these methods claim to construct complex networks that preserve certain properties of the underlying dynamical system, and hence, they mark new ways of accessing quantitative indicators based on that dynamics. In this paper, we test this assertion by developing an algorithm to realize dynamical systems from these complex networks in such a way that trajectories of these dynamical systems produce time series that preserve certain statistical properties of the original time series (and hence, also the underlying true dynamical system). Trajectories from these networks are constructed from only the information in the network and are shown to be statistically equivalent to the original time series. In the context of this algorithm, we are able to demonstrate that the so-called adaptive k-nearest neighbour algorithm for generating networks out-performs methods based on -ball recurrence plots. For such networks, and with a suitable choice of parameter values, which we provide, the time series generated by this method function as a new kind of nonlinear surrogate generation algorithm. With this approach, we are able to test whether the simulation dynamics built from a complex network capture the underlying structure of the original system; whether the complex network is an adequate model of the dynamics.

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“…An improved version of the AAFT algorithm has been suggested by Schreiber and Schmitz [8,9] using an iterative scheme called the IAAFT surrogates, which is reported to be more consistent to test null hypothesis [7]. Recently, Nakamura et al [10] have proposed a surrogate generation method called Truncated Fourier Transform (TFT) [11]. However, the surrogate data generated by this method are influenced by a cut-off frequency.…”

Section: Introductionmentioning

confidence: 99%

Recurrence network measures for hypothesis testing using surrogate data: Application to black hole light curves

Jacob

Harikrishnan

Misra

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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Recurrence networks and the associated statistical measures have become important tools in the analysis of time series data. In this work, we test how effective the recurrence network measures are in analyzing real world data involving two main types of noise, white noise and colored noise. We use two prominent network measures as discriminating statistic for hypothesis testing using surrogate data for a specific null hypothesis that the data is derived from a linear stochastic process. We show that the characteristic path length is especially efficient as a discriminating measure with the conclusions reasonably accurate even with limited number of data points in the time series. We also highlight an additional advantage of the network approach in identifying the dimensionality of the system underlying the time series through a convergence measure derived from the probability distribution of the local clustering coefficients. As examples of real world data, we use the light curves from a prominent black hole system and show that a combined analysis using three primary network measures can provide vital information regarding the nature of temporal variability of light curves from different spectroscopic classes.

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Testing for nonlinearity in irregular fluctuations with long-term trends

Cited by 41 publications

References 20 publications

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

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

Dynamical Systems Induced on Networks Constructed from Time Series

Recurrence network measures for hypothesis testing using surrogate data: Application to black hole light curves

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