Characterizing and detecting changes in complex multidimensional data with permutation entropy

Author: Juan Gancio Vázquez

Title: Characterizing and detecting changes in complex multidimensional data with permutation entropy

Supervisors: Masoller Alonso, Cristina (director);  Tirabassi, Giulio (co-director).

Presentation date: 14th February 2025

Link to text: https://www.tesisenred.net/handle/10803/693894

Abstract:

The analysis of signals obtained from complex dynamical systems is very important, not only from the point of view of many practical and interdisciplinary applications, but also, from the point of view of fundamental science, for elucidating the underlying mechanisms that generate complex behaviors. On one side, large amounts of data are currently used for purposes that have significant impact on society, for example, the detection and prediction of epidemic spreads, the analysis of trends in mobility and transportation networks, weather forecasting, to name a few. On the other side, many of the most challenging scientific endeavors intend to untangle many of these complex systems, such as the global climate and the human brain, and rely on the analysis of the signals that can be extracted from them. The analysis of these signals, even using modern approaches like machine learning and artificial intelligence, is based on the extraction of features that encode the relevant information that one needs for the specific end.

One of the possible techniques used to extract features is ordinal analysis, which was proposed more than 20 years ago and looks at the relative ordering of data points to determine different aspects of the systems, like how predictable, complex, or efficient they are. Although it has been extensively applied to a wide variety of systems, and generalized to include additional aspects of the data, as well to extract temporal and spatial features, there are still aspects of its implementation to be addressed. The main goal of this thesis is to demonstrate new applications of ordinal pattern analysis for uncovering temporal and spatial structures in real world complex data. Specifically, I analyze experimental recordings obtained during the turn-on of a complex multimode laser; I analyze EEG signals recorded from healthy subjects in different conditions (eyes open or eyes open) and I analyze and compare sea surface temperature anomalies of two well-known climate datasets, in two important geography regions (El Niño and Gulf Stream).

In the first chapter of the results section, I present the experimental analysis of a long cavity semiconductor laser in order to anticipate and identify the threshold bifurcation that occurs during its turn on.

In the second chapter of the results section, I present the analysis of brain data obtained from electroencephalograms (EEG): recordings of the brains electrical activity obtained from the scalp in two conditions, the subjects having their eyes open (EO) or their eyes closed (EC). Here I show how the temporal and spatial features perform in the classification between the EO and EC states, and how, for the spatial features, evaluating the correlations with specific orientations can improve this performance.

Finally, in the final chapter of the results section, I analyze two datasets of sea surface temperature anomaly, and I show how the spatial features allow the detection of transitions caused by changes in the acquisition and processing methodology of these datasets, showing also how their agreement improves with time.

Taken together, the studies carried out in this thesis demonstrate that ordinal analysis offers great flexibility, allowing the selection of different time scales, different spatial scales, or different shapes and orientations of patterns, which allows to obtain relevant features that encapsulate complementary information to characterize complex spatio-temporal data.