Contributions to the Study of Time Series and Images with the Entropy-Complexity Plane - Chagas, Eduarda T. C.; Ramos, Heitor S.; Frery, Alejandro C. (Anais do Concurso de Teses e Dissertações da SBC (CTD-SBC); 2022: Anais do XXXV Concurso de Teses e Dissertações, 2022)
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.