Contributions to the Study of Time Series and Images with the Entropy-Complexity Plane

  • Eduarda T. C. Chagas UFMG
  • Heitor S. Ramos UFMG
  • Alejandro C. Frery Victoria University of Wellington

Resumo


In the context of non-parametric analysis of time series, the use of Ordinal Patterns combined with descriptors of Information Theory proved being powerful in characterizing processes underlying the data dynamics. Two are prominent among those descriptors: Shannon's entropy and Statistical Complexity; together, they define the Entropy-Complexity Plane (HC). Although powerful, this approach suffers from two major shortcomings: (i) there are no statistical tests, and (ii) there is some loss of valuable information when discarding the signal amplitude. This work brings solutions to those problems with (I) empirical tests in the HC plane, and (II) a modification in the transition graph of ordinal patterns, the Weighted Amplitude Transition Graph, which weights its edges using amplitude information. We show applications to white noise analysis, and to discrimination and classification of textures in remotely-sensed images. We also provide the code and data that promote reproducibility and replicability of these results.

Palavras-chave: Bandt-Pompe Symbolization, Ordinal Patterns, Complexity-entropy Plane, Information theory

Referências

Bandt, C. and Pompe, B. (2002). Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88:174102-1-174102-4.

Barros, P. H., Queiroz, F., Figueredo, F., dos Santos, J. A., and Ramos, H. S. (2020). A new similarity space tailored for supervised deep metric learning.

Chan, T. M. and Har-Peled, S. (2020). Smallest k-enclosing rectangle revisited. Discrete & Computational Geometry.

De Micco, L., González, C. M., Larrondo, H. A., Martin, M. T., Plastino, A., and Rosso, O. A. (2008). Randomizing nonlinear maps via symbolic dynamics. Physica A: Statistical Mechanics and its Applications, 387(14):3373-3383.

Gabriel, C., Wittmann, C., Sych, D., Dong, R., Mauerer, W., Andersen, U. L., Marquardt, C., and Leuchs, G. (2010). A generator for unique quantum random numbers based on vacuum states. Nature Photonics, 4(10):711-715.

Haahr, M. (1998-2018). RANDOM.ORG: true random number service. https://www.random.org. Accessed: 2018-06-01.

Larrondo, H. A., Martín, M. T., González, C. M., Plastino, A., and Rosso, O. A. (2006). Random number generators and causality. Physics Letters A, 352(4-5):421-425.

Lee, J.-H. and Hsueh, Y.-C. (1994). Texture classification method using multiple space filling curves. Pattern Recognit. Lett., 15(12):1241-1244.

López-Ruiz, R., Mancini, H., and Calbet, X. (1995). A statistical measure of complexity. Physics Letters A, 209(5-6):321-326.

Rousseeuw, P. J., Ruts, I., and Tukey, J.W. (1999). The bagplot: A bivariate boxplot. The American Statistician, 53(4):382.
Publicado
31/07/2022
Como Citar

Selecione um Formato
CHAGAS, Eduarda T. C.; RAMOS, Heitor S.; FRERY, Alejandro C.. Contributions to the Study of Time Series and Images with the Entropy-Complexity Plane. In: CONCURSO DE TESES E DISSERTAÇÕES (CTD), 35. , 2022, Niterói. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 111-120. ISSN 2763-8820. DOI: https://doi.org/10.5753/ctd.2022.222888.