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- Title
Characterizing Complex Spatiotemporal Patterns from Entropy Measures.
- Authors
Barauna, Luan Orion; Sautter, Rubens Andreas; Rosa, Reinaldo Roberto; Rempel, Erico Luiz; Frery, Alejandro C.
- 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 ( S H p ) and a new approach based on Tsallis Spectral Permutation Entropy ( S q s ). Notably, our observations reveal the segregation of reaction terms in this S H p × S q s 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.
- Subjects
MACHINE learning; SPATIOTEMPORAL processes; PLASMA turbulence; ENTROPY; UNCERTAINTY (Information theory); STATISTICAL thermodynamics; TIME series analysis
- Publication
Entropy, 2024, Vol 26, Issue 6, p508
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e26060508