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Sur les Propriétés Statistiques de l'Entropie de Permutation Multi-échelle et ses Raffinements; applications sur les Signaux Électromyographiques de Surface

Abstract : Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) are extensively used in the analysis of time series searching for regularities, particularly in the context of biomedical signal. The researchers need to find optimal interpretations, which can be compromised by not taking in account the properties of the MPE algorithm, particularly regarding its statistical properties.Therefore, in the present work we expand on the statistical theory behind MPE, particularly regarding to the characterization of its first two moments in the context of multiscaling. We then explore the composite versions of MPE, in order to understand the underlying properties behind their improved performance. We also tested the expected MPE values for widely used Gaussian stochastic processes, which allows to obtain an Entropy benchmark when using these models to simulate real signals. Finally, we apply both the classical and composite MPE methods on surface Electromyographic (sEMG) data, in order to differentiate different muscle activity dynamics in isometric contractions.As a result of our project, we found the MPE to be a biased statistic, which decreases respect to the multiscaling factor regardless of the signals probability distribution. We found the MPE statistic’s variance to be highly dependent to the value of MPE itself, and almost equal to its Cramér-Rao Lower Bound, which means it is an efficient estimator. We found the composite versions, albeit an improvement, also measure reduntant information, which modifies the MPE estimation. In response, we provided a new algorithm as an alternative to the coarse-grain multiscaling, which further improve the estimations.When applied to general correlated Gaussian models, we found the MPE to be completely characterized by the model parameters. Thus, we developed a general formulation for the expected MPE for low embedding dimensions. When we applied to real sEMG signals, we were able to distinguish between fatigue and non-fatigue states with all methods, particularly for high embedding dimensions. Moreover, we found our proposed MPE method to enhance de difference between activity states.Therefore, we provide the reader with not only a development over the current MPE theory, but also with the implications of these findings, both in the context of modelization, and the application of these techniques in the biomedical field.
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Antonio Davalos Trevino. Sur les Propriétés Statistiques de l'Entropie de Permutation Multi-échelle et ses Raffinements; applications sur les Signaux Électromyographiques de Surface. Autre. Université d'Orléans, 2020. Français. ⟨NNT : 2020ORLE3102⟩. ⟨tel-03219292⟩

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