In this paper we illustrate the potential of ordinal-patterns-based methods for analysis of real-world data and, especially, of electroencephalogram (EEG) data. We apply already known (empirical permutation entropy, ordinal pattern distributions) and new (empirical conditional entropy of ordinal patterns, robust to noise empirical permutation entropy) methods for measuring complexity, segmentation and classification of time series.

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given ordinal pattern. We observe that this quantity provides a good estimation of the Kolmogorov-Sinai entropy in many cases. In particular, the conditional entropy of ordinal patterns of a finite order coincides with the Kolmogorov-Sinai entropy for periodic dynamics and for Markov shifts over a binary alphabet. Finally, the conditional entropy of ordinal patterns is computationally simple and thus can be well applied to real-world data.

Since Bandt et al. have shown that the permutation entropy and the Kolmogorov-Sinai entropy coincide for piecewise monotone interval maps, the relationship of both entropies for time-discrete dynamical systems is of a certain interest. The aim of this paper is a discussion of this relationship on the basis of an ordinal characterization of the Kolmogorov-Sinai entropy recently given.

Objective: to establish an algorithmic framework and a benchmark dataset for comparing methods of pulse rate estimation using imaging photoplethysmography (iPPG). Approach: first we reveal essential steps of pulse rate estimation from facial video and review methods applied at each of the steps. Then we investigate performance of these methods for DEAP dataset www.eecs.qmul. ac.uk/mmv/datasets/deap/ containing facial videos and reference contact photoplethysmograms. Main results: best assessment precision is achieved when pulse rate is estimated using continuous wavelet transform from iPPG extracted by the POS method (overall mean absolute error below 2 heart beats per minute). Significance: we provide a generic framework for theoretical comparison of methods for pulse rate estimation from iPPG and report results for the most popular methods on a publicly available dataset that can be used as a benchmark.