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Barauna LO, Sautter RA, Rosa RR, Rempel EL, Frery AC. Characterizing Complex Spatiotemporal Patterns from Entropy Measures. ENTROPY (BASEL, SWITZERLAND) 2024; 26:508. [PMID: 38920517 PMCID: PMC11202814 DOI: 10.3390/e26060508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Revised: 03/02/2024] [Accepted: 03/08/2024] [Indexed: 06/27/2024]
Abstract
In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp×Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns.
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Affiliation(s)
- Luan Orion Barauna
- Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, São José dos Campos 12227-010, SP, Brazil; (R.A.S.); (R.R.R.)
| | - Rubens Andreas Sautter
- Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, São José dos Campos 12227-010, SP, Brazil; (R.A.S.); (R.R.R.)
| | - Reinaldo Roberto Rosa
- Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, São José dos Campos 12227-010, SP, Brazil; (R.A.S.); (R.R.R.)
- Laboratory for Computing and Applied Math, National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, São José dos Campos 12227-010, SP, Brazil
| | - Erico Luiz Rempel
- Mathematics Department, Aeronautics Institute of Technology, Praça Marechal Eduardo Gomes, 50, Vila das Acácias, São José dos Campos 12228-900, SP, Brazil;
| | - Alejandro C. Frery
- School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand;
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