Study of the ability of permutation entropy measures to detect changes in high-dimensional data sets

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. 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. 

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 closed) 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).

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.