Combining Measures of Signal Complexity and Machine Learning for Time Series Analyis: A Review

Raubitzek, Sebastian; Neubauer, Thomas

doi:10.3390/e23121672

Cited by 18 publications

(10 citation statements)

References 93 publications

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“…Fractal dimension and Hurst exponent analysis are based on a different theoretical framework than entropy-based methods, and they can be found as complexity measures in functional MRI studies (Bullmore et al, 2009;Tagliazucchi et al, 2013;Dong et al, 2018), EEG studies (Linkenkaer-Hansen et al, 2001;Raghavendra et al, 2009;Sabeti et al, 2009;Holloway et al, 2014), but also outside brain research (Raubitzek and Neubauer, 2021).…”

Section: Hurst Exponentsmentioning

confidence: 99%

Complexity measures for EEG microstate sequences - concepts and algorithms

Wegner

Wiemers

Hermann

et al. 2023

Preprint

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EEG microstate sequence analysis quantifies properties of ongoing brain electrical activity which is known to exhibit complex dynamics across many time scales. In this report we review recent developments in quantifying microstate sequence complexity, we classify these approaches with regard to different complexity concepts, and we evaluate excess entropy as a yet unexplored quantity in microstate research. We determined the quantities entropy rate, excess entropy, Lempel-Ziv complexity (LZC), and Hurst exponents on Potts model data, a discrete statistical mechanics model with a temperature-controlled phase transition. We then applied the same techniques to EEG microstate sequences from wakefulness and non-REM sleep stages and used first-order Markov surrogate data to determine which time scales contributed to the different complexity measures. We demonstrate that entropy rate and LZC measure the Kolmogorov complexity (randomness) of microstate sequences, whereas excess entropy and Hurst exponents describe statistical complexity which attains its maximum at intermediate levels of randomness. We confirmed the equivalence of entropy rate and LZC when the LZ-76 algorithm is used, a result previously reported for neural spike train analysis (Amigó et al. 2004). Surrogate data analyses prove that entropy-based quantities and LZC focus on short-range temporal correlations, whereas Hurst exponents include short and long time scales. Sleep data analysis reveals that deeper sleep stages are accompanied by a decrease in Kolmogorov complexity and an increase in statistical complexity. Regarding the practical use of these methods, we suggest that LZC can be used as an efficient entropy rate estimator that avoids the estimation of joint entropies, whereas entropy rate estimation via joint entropies has the advantage of providing excess entropy as the second parameter of the same linear fit. We conclude that metrics of statistical complexity are a useful addition to microstate analysis and address a complexity concept that is not yet covered by existing microstate algorithms while being actively explored in other areas of brain research.

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Section: Hurst Exponentsmentioning

confidence: 99%

Complexity measures for EEG microstate sequences - concepts and algorithms

Wegner

Wiemers

Hermann

et al. 2023

Preprint

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“…It must be noted that non-linear extensions of G-causality can be computationally expensive [ 66 ]; however, according to Granger, non-linear models reflect a more proper approach to model practical problems, which are inherently non-linear [ 70 ]. Since Schreiber transfer entropy is a non-linear approach, it can be used to measure ‘causality’ using non-linear data [ 71 ]. In this sub-section, this paper investigates non-linear Schreiber transfer entropy and its relationship with G-causality for the KLFIN.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Entropy is measuring any information uncertainty, diversity or randomness [ 71 ]. Low entropy implies that information uncertainty is low.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The transfer entropy notation of

measures the information flow from

or a pair of constituents; if the transfer entropy value is positive for

is seen as reducing the degree of uncertainties of

[ 65 ], and therefore having a causal effect to

[ 76 ], which is intuitively similar in a G-causality sense. The larger the value is, the greater the reduction of uncertainties [ 71 ], i.e., the higher the causality.…”

Section: Literature Reviewmentioning

confidence: 99%

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The Causality and Uncertainty of the COVID-19 Pandemic to Bursa Malaysia Financial Services Index’s Constituents

Zuhud

Musa

Ismail

et al. 2022

Entropy

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Valued in hundreds of billions of Malaysian ringgit, the Bursa Malaysia Financial Services Index’s constituents comprise several of the strongest performing financial constituents in Bursa Malaysia’s Main Market. Although these constituents persistently reside mostly within the large market capitalization (cap), the existence of the individual constituent’s causal influence or intensity relative to each other’s performance during uncertain or even certain times is unknown. Thus, the key purpose of this paper is to identify and analyze the individual constituent’s causal intensity, from early 2018 (pre-COVID-19) to the end of the year 2021 (post-COVID-19) using Granger causality and Schreiber transfer entropy. Furthermore, network science is used to measure and visualize the fluctuating causal degree of the source and the effected constituents. The results show that both the Granger causality and Schreiber transfer entropy networks detected patterns of increasing causality from pre- to post-COVID-19 but with differing causal intensities. Unexpectedly, both networks showed that the small- and mid-caps had high causal intensity during and after COVID-19. Using Bursa Malaysia’s sub-sector for further analysis, the Insurance sub-sector rapidly increased in causality as the year progressed, making it one of the index’s largest sources of causality. Even after removing large amounts of weak causal intensities, Schreiber transfer entropy was still able to detect higher amounts of causal sources from the Insurance sub-sector, whilst Granger causal sources declined rapidly post-COVID-19. The method of using directed temporal networks for the visualization of temporal causal sources is demonstrated to be a powerful approach that can aid in investment decision making.

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“…There are many techniques for estimating entropy of time series, such as sample entropy, approximate entropy, Kolmogorov-Sinai (K-S) entropy, the K 2 entropy, and the multiscale entropy. K-S and the K 2 entropy require a large amount of data for proper complexity quantification (Raubitzek and Neubauer 2021). Approximate entropy and sample entropy, however, can deal with short-length signals (Richman and Moorman 2000).…”

Section: Introductionmentioning

confidence: 99%

Temporal complexity of EEG encodes human alertness

Hadra¹,

Omidvarnia²,

Mesbah³

2022

Physiol. Meas.

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Objective: Automatic human alertness monitoring has recently become an important research topic with important applications in many areas such as the detection of drivers’ fatigue, monitoring of monotonous tasks that require a high level of alertness such as traffic control and nuclear power plant monitoring, and sleep staging. In this study, we propose that balanced dynamics of Electroencephalography (EEG) (so called EEG temporal complexity) is a potentially useful feature for identifying human alertness states. Recently, a new signal entropy measure, called Range Entropy (RangeEn), was proposed to overcome some limitations of two of the most widely used entropy measures, namely Approximate Entropy (ApEn) and Sample Entropy (SampEn), and showed its relevance for the study of time domain EEG complexity. In this paper, we investigated whether the RangeEn holds discriminating information associated with human alertness states, namely Awake, Drowsy, and Sleep and compare its performance against those of SampEn and ApEn. Approach: We used EEG data from 60 healthy subjects of both sexes and different ages acquired during whole night sleeps. Using a 30-second sliding window, we computed the three entropy measures of EEG and performed statistical analyses to evaluate the ability of these entropy measures to discriminate among the different human alertness states. Main results: Although the three entropy measures contained useful information about human alertness, RangeEn showed a higher discriminative capability compared to ApEn and SampEn especially when using EEG within the Beta frequency band. Significance: Our findings highlight the EEG temporal complexity evolution through the human alertness states. This relationship can potentially be exploited for the development of automatic human alertness monitoring systems and diagnostic tools for different neurological and sleep disorders, including insomnia.

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Combining Measures of Signal Complexity and Machine Learning for Time Series Analyis: A Review

Cited by 18 publications

References 93 publications

Complexity measures for EEG microstate sequences - concepts and algorithms

Complexity measures for EEG microstate sequences - concepts and algorithms

The Causality and Uncertainty of the COVID-19 Pandemic to Bursa Malaysia Financial Services Index’s Constituents

Temporal complexity of EEG encodes human alertness

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