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A generalized permutation entropy for noisy dynamics and random processes


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Title:
A generalized permutation entropy for noisy dynamics and random processes
Authors:
AMIGO, JOSE M.  
Dale, Roberto  
Tempesta, Piergiulio  
Editor:
American Institute of Physics
Department:
Departamentos de la UMH::Estadística, Matemáticas e Informática
Issue Date:
2021-01-06
URI:
https://hdl.handle.net/11000/30686
Abstract:
Permutation entropy measures the complexity of a deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or simply permutations. Reasons for the increasing popularity of this entropy in time series analysis include that (i) it converges to the Kolmogorov–Sinai entropy of the underlying dynamics in the limit of ever longer permutations and (ii) its computation dispenses with generating and ad hoc partitions. However, permutation entropy diverges when the number of allowed permutations grows super-exponentially with their length, as happens when time series are output by dynamical systems with observational or dynamical noise or purely random processes. In this paper, we propose a generalized permutation entropy, belonging to the class of group entropies, that is finite in that situation, which is actually the one found in practice. The theoretical results are illustrated numerically by random processes with short- and long-term dependencies, as well as by noisy deterministic signals.
Keywords/Subjects:
Logistic map
Entropy
Signal processing
Statistical mechanics
Stochastic processes
Time series analysis
Brownian motion
Knowledge area:
CDU: Generalidades.: Ciencia y tecnología de los ordenadores. Informática.
Type of document:
application/pdf
Access rights:
info:eu-repo/semantics/closedAccess
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
DOI:
https://doi.org/10.1063/5.0023419
Appears in Collections:
Artículos Estadística, Matemáticas e Informática



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