Parameter Selection for Permutation Entropy Measurements

Staniek, Matthäus; Lehnertz, Klaus

doi:10.1142/s0218127407019652

Cited by 109 publications

(69 citation statements)

References 9 publications

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“…Our simulations show that increasing m beyond 4 affects the running time without significantly changing the obtained entropies. This is inline with the findings in [16] where the parameter selection problem has been addressed and [14]. For situations where the effect of m is more pronounced, the running time issue can be addressed by speeding up the sliding of the window as this entails a higher number of affected patterns at each instance.…”

Section: B Single-channel Eeg Data Analysissupporting

confidence: 63%

Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information

et al. 2013

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Permutation entropy (PE) has been recently suggested as a novel measure to characterize the complexity of nonlinear time series. In this paper, we propose a simple method to address some of PE's limitations, mainly its inability to differentiate between distinct patterns of a certain motif, and the sensitivity of patterns close to the noise floor. The method relies on the fact that patterns may be too disparate in amplitudes and variances and proceeds by assigning weights for each extracted vector when computing the relative frequencies associated with every motif. Simulations were conducted over synthetic and real data for a weighting scheme inspired by the variance of each pattern. Results show better robustness and stability in the presence of higher levels of noise, in addition to a distinctive ability to extract complexity information from data with spiky features or having abrupt changes in magnitude.

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Section: B Single-channel Eeg Data Analysissupporting

confidence: 63%

Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information

et al. 2013

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“…must be satisfied in order to obtain a reliable estimation of the spectrum. 31 For practical purposes, BP suggest in their cornerstone paper 20 to estimate the frequency of ordinal patterns with 3 D 7 and time lag s ¼ 1 (consecutive points). Nevertheless, other values of s > 1 (non-consecutive points) might provide additional relevant information as has been recently shown.…”

Section: Permutation Spectrum Testmentioning

confidence: 99%

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

Kulp

Zunino

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism. The importance of distinguishing between periodic, chaotic, and stochastic dynamics from time series analysis is well-recognized for understanding the mechanisms that govern the regarded complex systems. In this work, we have introduced a conceptually simple and computationally fast symbolic visual test for discriminating chaotic and stochastic dynamics, called the permutation spectrum test. Because the symbolization is made by implementing the Bandt and Pompe methodology, all the advantages associated with this natural encoding (simplicity, extremely fast calculation, robustness, and invariance with respect to monotonous transformations) are inherited by the permutation spectrum test. We have shown that this pragmatic approach is robust in situations in which other tests fail. We have also confirmed its practical utility by examining several experimental and natural time series.

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“…Its choice depends on the length N of the time series in such a way that the condition N D! must be satisfied in order to obtain reliable statistics [15]. It is worth remarking that there are D!…”

Section: Multiscale Complexity-entropy Causality Planementioning

confidence: 99%

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach

2012

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In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.

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Parameter Selection for Permutation Entropy Measurements

Cited by 109 publications

References 9 publications

Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information

Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach

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