Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen-Shannon Distance

Taking into account the complexity of the human brain dynamics, the appropriate characterization of any brain state is a challenge not easily met. Actually, even the discrimination of simple behavioral tasks, such as resting with eyes closed or eyes open, represents an intricate problem and many efforts have been and are being made to overcome it. In this work, the aforementioned issue is carefully addressed by performing multiscale analyses of electroencephalogram records with the permutation Jensen-Shannon distance. The influence that linear and nonlinear temporal correlations have on the discrimination is unveiled. Results obtained lead to significant conclusions that help to achieve an improved distinction between these resting brain states.

Quantifying the diversity of multiple time series with an ordinal symbolic approach

The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes. This ordinal tool also serves to identify optimal operating conditions in the machine learning approach of reservoir computing. These results allow us to envision potential applications for the handling and characterization of large amounts of data, paving the way for addressing some of the most pressing issues facing the current big data paradigm.

Irreversibility of symbolic time series: A cautionary tale

Many empirical time series are genuinely symbolic: Examples range from link activation patterns in network science, to DNA coding or firing patterns in neuroscience, to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility-the difference between forward and backward statistics in stationary time series-is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series-a classical way to encode chaotic trajectories via symbolic dynamics. In this paper we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis-and interpretation-of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of nonpalindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m<4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map.

Rao-Burbea centroids applied to the statistical characterization of time series and images through ordinal patterns

Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects, such as time series, networks, and images. Notably, not every divergence provides identical results when applied to the same problem. Therefore, it seems convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice, an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work, we choose the family of divergences known as the Burbea-Rao centroids (BRCs). For the mapping of the original time series into a symbolic sequence, we work with the ordinal pattern scheme. We apply our proposals to analyze simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen-Shannon divergence, besides the fact that it verifies some interesting formal properties.

Ordinal analysis of lexical patterns

Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words. Using an ordinal pattern approach, we present an analysis of lexical statistical connections for 11 major languages. We find that the diverse manners that languages utilize to express word relations give rise to unique pattern structural distributions. Furthermore, fluctuations of these pattern distributions for a given language can allow us to determine both the historical period when the text was written and its author. Taken together, our results emphasize the relevance of ordinal time series analysis in linguistic typology, historical linguistics, and stylometry.

Markov-modulated model for landing flow dynamics: An ordinal analysis validation

Air transportation is a complex system characterized by a plethora of interactions at multiple temporal and spatial scales; as a consequence, even simple dynamics like sequencing aircraft for landing can lead to the appearance of emergent behaviors, which are both difficult to control and detrimental to operational efficiency. We propose a model, based on a modulated Markov jitter, to represent ordinal pattern properties of real landing operations in European airports. The parameters of the model are tuned by minimizing the distance between the probability distributions of ordinal patterns generated by the real and synthetic sequences, as estimated by the Permutation Jensen-Shannon Distance. We show that the correlation between consecutive hours in the landing flow changes between airports and that it can be interpreted as a metric of efficiency. We further compare the dynamics pre and post COVID-19, showing how this has changed beyond what can be attributed to a simple reduction of traffic. We finally draw some operational conclusions and discuss the applicability of these findings in a real operational environment.

Generation of Individualized Synthetic Data for Augmentation of the Type 1 Diabetes Data Sets Using Deep Learning Models

In this paper, we present a methodology based on generative adversarial network architecture to generate synthetic data sets with the intention of augmenting continuous glucose monitor data from individual patients. We use these synthetic data with the aim of improving the overall performance of prediction models based on machine learning techniques. Experiments were performed on two cohorts of patients suffering from type 1 diabetes mellitus with significant differences in their clinical outcomes. In the first contribution, we have demonstrated that the chosen methodology is able to replicate the intrinsic characteristics of individual patients following the statistical distributions of the original data. Next, a second contribution demonstrates the potential of synthetic data to improve the performance of machine learning approaches by testing and comparing different prediction models for the problem of predicting nocturnal hypoglycemic events in type 1 diabetic patients. The results obtained for both generative and predictive models are quite encouraging and set a precedent in the use of generative techniques to train new machine learning models.