Detection of weak transitions in signal dynamics using recurrence time statistics

Gao, Jianbo; Cao, Yinhe; Gu, Lingjia; Harris, John G.; Principe, J.C.

doi:10.1016/j.physleta.2003.08.018

Cited by 44 publications

(22 citation statements)

References 17 publications

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“…In this work, we have used nonlinear methods namely fractal dimension (FD) [16] , largest Lyapunov exponent (LLE) [17] , sample entropy (SampEnt) [18] , DFA [19] , Hurst's exponent (H) [20] , higher order spectra features (weighted centre of bispectrum (W_Bx, W_By), bispectrum phase entropy (EntPh) normalized bispectral entropy (Ent1) and normalized bispectral squared entropies (Ent2, Ent3)) [21] , and recurrence quantification analysis parameters (determinism (DET), entropy (ENTR), laminarity (LAM), and recurrence times (T2)) [22] . These extracted features are ranked using the t value [23] . In this work, we have extracted 15 features.…”

Section: Feature Extraction and Rankingmentioning

confidence: 99%

A Novel Depression Diagnosis Index Using Nonlinear Features in EEG Signals

Acharya

Sudarshan²,

Adeli³

et al. 2015

Eur Neurol

219

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Depression is a mental disorder characterized by persistent occurrences of lower mood states in the affected person. The electroencephalogram (EEG) signals are highly complex, nonlinear, and nonstationary in nature. The characteristics of the signal vary with the age and mental state of the subject. The signs of abnormality may be invisible to the naked eyes. Even when they are visible, deciphering the minute changes indicating abnormality is tedious and time consuming for the clinicians. This paper presents a novel method for automated EEG-based diagnosis of depression using nonlinear methods: fractal dimension, largest Lyapunov exponent, sample entropy, detrended fluctuation analysis, Hurst's exponent, higher order spectra, and recurrence quantification analysis. A novel Depression Diagnosis Index (DDI) is presented through judicious combination of the nonlinear features. The DDI calculated automatically based on the EEG recordings can be used to diagnose depression objectively using just one numeric value. Also, these features extracted from nonlinear methods are ranked using the t value and fed to the support vector machine (SVM) classifier. The SVM classifier yielded the highest classification performance with an average accuracy of about 98%, sensitivity of about 97%, and specificity of about 98.5%.

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Section: Feature Extraction and Rankingmentioning

confidence: 99%

A Novel Depression Diagnosis Index Using Nonlinear Features in EEG Signals

Acharya

Sudarshan²,

Adeli³

et al. 2015

Eur Neurol

219

View full text Add to dashboard Cite

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“…[50][51][52][53] Third, recurrence time statistics (i.e., the analysis of the distribution pðsÞ of time differences between the system leaving and reentering the neighborhood of a specific state vector) allows distinguishing different types of dynamic behavior. [54][55][56] Finally, e-recurrence networks (RNs) provide a graphtheoretical framework for quantifying various aspects of the underlying attractor's geometry. 29,[57][58][59][60][61][62][63][64][65][66][67] In the following, we will use pðsÞ and K 2 for further characterizing the dynamical complexity of the observed electrochemical oscillations.…”

Section: -5mentioning

confidence: 99%

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Zou

Donner

Wickramasinghe

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic complexity with increasing temperature of the system, resulting in a larger relative spread of the attractor in phase space. By allowing for feasible coordinate transformations, we demonstrate that the system, however, remains phase-coherent over the whole considered parameter range. This finding motivates a critical review of existing definitions of phase coherence that are exclusively based on dynamical characteristics and are thus potentially sensitive to projection effects in phase space. In contrast, referring to the attractor geometry, the gradual changes in some fundamental properties of the system commonly related to its phase coherence can be alternatively studied from a purely structural point of view. As a prospective example for a corresponding framework, recurrence network analysis widely avoids undesired projection effects that otherwise can lead to ambiguous results of some existing approaches to studying phase coherence. Our corresponding results demonstrate that since temperature increase induces more complex chaotic chemical reactions, the recurrence network properties describing attractor geometry also change gradually: the bimodality of the distribution of local clustering coefficients due to the attractor’s band structure disappears, and the corresponding asymmetry of the distribution as well as the average path length increase.

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“…In contrast to return times with respect to a fixed Poincaré surface, recurrence times refer to the time intervals after which the trajectory enters the ε-neighborhood of a previously visited point in phase space. Gao et al [33] demonstrated that similar to some line-based RQA measures, characteristics based on the RT distributions p(τ ) can be used for detecting subtle dynamical transitions, which motivated using a corresponding approach for testing against stationarity [34,35]. Besides their immediate importance for studies on extreme events [36], recurrence times have also proven their potential for the estimation of dynamical invariants such as the information dimension [30] and the Kolmogorov-Sinai entropy [37].…”

Section: A Recurrence Time Statisticsmentioning

confidence: 99%

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Zou

Donner

Kurths

2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral-and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given. PACS numbers:Oscillatory processes can be frequently observed in natural and technological systems. Often, the corresponding dynamics is not strictly periodic, but shows more complex temporal variability patterns characterized by a fast divergence of trajectories with arbitrarily close initial conditions [1-3]. There are numerous examples of such chaotic oscillators for which long-term predictions of amplitudes and phases are not possible. Therefore, studying their phase dynamics has recently attracted particular interest, e.g., regarding the process of phase synchronization between different coupled systems [4,5]. However, most existing methods suitable for this purpose require the explicit definition of an appropriate phase variable, which can become a non-trivial problem in the case of noncoherent chaotic oscillations. Therefore, studying the phase coherence properties of chaotic systems has become an important problem in both theoretical and experimental studies [6]. In this work, we propose some methods based on the concept of recurrences in phase space, which allow studying complementary aspects of chaotic oscillators relating to the geometric structure of, and the dynamics on the attractor. Specifically, we derive a detailed characterization of changes of the geometric structure of complex systems in phase space with varying control parameter, which accompany transitions from phase-coherent to noncoherent dynamics.

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Detection of weak transitions in signal dynamics using recurrence time statistics

Cited by 44 publications

References 17 publications

A Novel Depression Diagnosis Index Using Nonlinear Features in EEG Signals

A Novel Depression Diagnosis Index Using Nonlinear Features in EEG Signals

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

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