1. Alternative Ways to Compare the Detendred Fluctuation Analysis and its Variants. Application to Visual Tunneling Detection
- Author
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Patrick Mazoyer, Pierrick Legrand, Bastien Berthelot, Jean-Marc André, Eric Grivel, Laboratoire de l'intégration, du matériau au système (IMS), Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Quality control and dynamic reliability (CQFD), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ecole Nationale Supérieure de Cognitique (ENSC), Institut Polytechnique de Bordeaux, COGNITIQUE, Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1-Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1, Thales (France), Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), and THALES [France]
- Subjects
Computer science ,Tunneling ,Hurst ,02 engineering and technology ,Correlation function (astronomy) ,DMA ,Square (algebra) ,Convolution ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,Artificial Intelligence ,Moving average ,0202 electrical engineering, electronic engineering, information engineering ,Electrical and Electronic Engineering ,Hurst exponent ,Applied Mathematics ,020206 networking & telecommunications ,Function (mathematics) ,DFA ,Computational Theory and Mathematics ,Signal Processing ,Detrended fluctuation analysis ,020201 artificial intelligence & image processing ,Computer Vision and Pattern Recognition ,Statistics, Probability and Uncertainty ,Algorithm ,Linear filter - Abstract
International audience; The detrended fluctuation analysis (DFA) and its variants such as the detrended moving average (DMA) are widely used to estimate the Hurst exponent. These methods are very popular as they do not require advanced skills in the field of signal processing and statistics while providing accurate results. As a consequence, a great deal of interest has been paid to compare them and to better understand their behaviors from a mathematical point of view. In this paper, our contribution is threefold. Firstly, we propose another variant avoiding the discontinuities between consecutive local trends of the DFA by a priori constraining them to be continuous. Secondly, we show that, in all these approaches, the square of the fluctuation function can be presented in a similar matrix form. When the process is wide-sense stationary (w.s.s.), the latter can be seen as the power of the output of a linear filtering whose frequency response depends on the given method. In the general case, an interpretation of the square of the fluctuation function is also given by expressing it as the convolution between the 2D-Fourier transform of two matrices, one whose elements correspond to the instantaneous correlation function of the signal and the other which depends on the detrending method. To end up, an illustration is provided in the field of avionics for the detection of the visual tunneling, a deleterious cognitive state.
- Published
- 2020
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