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Yao W. Permutation time irreversibility in sleep electroencephalograms: Dependence on sleep stage and the effect of equal values. Phys Rev E 2024; 109:054104. [PMID: 38907450 DOI: 10.1103/physreve.109.054104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Accepted: 04/05/2024] [Indexed: 06/24/2024]
Abstract
Time irreversibility (TIR) refers to the manifestation of nonequilibrium brain activity influenced by various physiological conditions; however, the influence of sleep on electroencephalogram (EEG) TIR has not been sufficiently investigated. In this paper, a comprehensive study on permutation TIR (pTIR) of EEG data under different sleep stages is conducted. Two basic ordinal patterns (i.e., the original and amplitude permutations) are distinguished to simplify sleep EEGs, and then the influences of equal values and forbidden permutation on pTIR are elucidated. To detect pTIR of brain electric signals, five groups of EEGs in the awake, stages I, II, III, and rapid eye movement (REM) stages are collected from the public Polysomnographic Database in PhysioNet. Test results suggested that the pTIR of sleep EEGs significantly decreases as the sleep stage increases (p<0.001), with the awake and REM EEGs demonstrating greater differences than others. Comparative analysis and numerical simulations support the importance of equal values. Distribution of equal states, a simple quantification of amplitude fluctuations, significantly increases with the sleep stage (p<0.001). If these equalities are ignored, incorrect probabilistic differences may arise in the forward-backward and symmetric permutations of TIR, leading to contradictory results; moreover, the ascending and descending orders for symmetric permutations also lead different outcomes in sleep EEGs. Overall, pTIR in sleep EEGs contributes to our understanding of quantitative TIR and classification of sleep EEGs.
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Affiliation(s)
- Wenpo Yao
- State Key Laboratory of Organic Electronics and Information Displays, Institute of Advanced Materials, School of Chemistry and Life Sciences, School of Geographic and Biologic Information, Nanjing University of Posts and Telecommunications, Nanjing 210023, China and Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai 200433, China
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Lu Y, Yao L, Li H, Kausar T, Zhang Z, Gao P, Wang M. A new network representation for time series analysis from the perspective of combinatorial property of ordinal patterns. Heliyon 2023; 9:e22455. [PMID: 38034738 PMCID: PMC10687224 DOI: 10.1016/j.heliyon.2023.e22455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2023] [Revised: 11/12/2023] [Accepted: 11/13/2023] [Indexed: 12/02/2023] Open
Abstract
Revealing system behavior from observed time series is a fundamental problem worthy of in-depth study and exploration, and has attracted extensive attention in a wide range of fields due to its wide application values. In this paper, we propose a novel network construction method for time series analysis, which is different from the existing ordinal network method concerning the transition probability of ordinal patterns in transition networks. The proposed network representation is based on the combinatorial property concerning the inversion number of ordinal patterns from the ordinal partitions of time series. For the proposed network construction method, the network nodes are represented by each ordinal partition of time series and the edge weight between network nodes is determined by a novel proximity relationship of ordinal patterns which is a newly defined metric based on the inversion number of ordinal patterns. Using random signals and chaotic signals as examples, we demonstrate the potential of the proposed network construction method for the network representation of time series. We also employ the proposed network construction method in quantitative EEG for the identification of three different physiological and pathological brain states. According to the results of AUC values, one can observe that the discriminating power of the AND of the proposed network construction method is slightly stronger than that of the available ordinal network. The experimental results illustrate that our proposed network construction method opens up a new pathway for network representation of time series, which is capable of quantifying time series for feature extraction and pattern learning for time series analysis.
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Affiliation(s)
- Yun Lu
- School of Computer Science and Engineering, Huizhou University, Huizhou, Guangdong 516007, China
| | - Longxin Yao
- School of Electronic and Information Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
| | - Heng Li
- School of Electronic and Information Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
| | - Tasleem Kausar
- Mirpur Institute of Technology, Mirpur University of Science and Technology, Mirpur, 10250, AJK, Pakistan
| | - Zhen Zhang
- School of Computer Science and Engineering, Huizhou University, Huizhou, Guangdong 516007, China
| | - Peng Gao
- School of Cyber Science and Engineering, Qufu Normal University, Shandong 273165, China
| | - Mingjiang Wang
- School of Electronic and Information Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
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Cuesta-Frau D, Kouka M, Silvestre-Blanes J, Sempere-Payá V. Slope Entropy Normalisation by Means of Analytical and Heuristic Reference Values. ENTROPY (BASEL, SWITZERLAND) 2022; 25:66. [PMID: 36673207 PMCID: PMC9858583 DOI: 10.3390/e25010066] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Revised: 12/22/2022] [Accepted: 12/23/2022] [Indexed: 06/17/2023]
Abstract
Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [0,1] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max-min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods.
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Affiliation(s)
- David Cuesta-Frau
- Technological Institute of Informatics (ITI), Universitat Politècnica de València, Alcoi Campus, 03801 Alcoi, Spain
| | - Mahdy Kouka
- Department of System Informatics and Computers, Universitat Politècnica de València, 46022 Valencia, Spain
| | - Javier Silvestre-Blanes
- Technological Institute of Informatics (ITI), Universitat Politècnica de València, Alcoi Campus, 03801 Alcoi, Spain
| | - Víctor Sempere-Payá
- Technological Institute of Informatics (ITI), Universitat Politècnica de València, Alcoi Campus, 03801 Alcoi, Spain
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Kouka M, Cuesta-Frau D. Slope Entropy Characterisation: The Role of the δ Parameter. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1456. [PMID: 37420476 DOI: 10.3390/e24101456] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Revised: 09/16/2022] [Accepted: 09/21/2022] [Indexed: 07/09/2023]
Abstract
Many time series entropy calculation methods have been proposed in the last few years. They are mainly used as numerical features for signal classification in any scientific field where data series are involved. We recently proposed a new method, Slope Entropy (SlpEn), based on the relative frequency of differences between consecutive samples of a time series, thresholded using two input parameters, γ and δ. In principle, δ was proposed to account for differences in the vicinity of the 0 region (namely, ties) and, therefore, was usually set at small values such as 0.001. However, there is no study that really quantifies the role of this parameter using this default or other configurations, despite the good SlpEn results so far. The present paper addresses this issue, removing δ from the SlpEn calculation to assess its real influence on classification performance, or optimising its value by means of a grid search in order to find out if other values beyond the 0.001 value provide significant time series classification accuracy gains. Although the inclusion of this parameter does improve classification accuracy according to experimental results, gains of 5% at most probably do not support the additional effort required. Therefore, SlpEn simplification could be seen as a real alternative.
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Affiliation(s)
- Mahdy Kouka
- Department of System Informatics and Computers, Universitat Politècnica de València, 03801 Alcoy, Spain
| | - David Cuesta-Frau
- Technological Institute of Informatics, Universitat Politècnica de València, 03801 Alcoy, Spain
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Jabloun M, Ravier P, Buttelli O. On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1343. [PMID: 37420363 DOI: 10.3390/e24101343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 09/12/2022] [Accepted: 09/14/2022] [Indexed: 07/09/2023]
Abstract
Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested.
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Affiliation(s)
- Meryem Jabloun
- Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orleans, 45100 Orleans, France
| | - Philippe Ravier
- Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orleans, 45100 Orleans, France
| | - Olivier Buttelli
- Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orleans, 45100 Orleans, France
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