Algorithmics, Possibilities and Limits of Ordinal Pattern Based Entropies

Entropy (Basel). 2019 May 29;21(6):547. doi: 10.3390/e21060547.


The study of nonlinear and possibly chaotic time-dependent systems involves long-term data acquisition or high sample rates. The resulting big data is valuable in order to provide useful insights into long-term dynamics. However, efficient and robust algorithms are required that can analyze long time series without decomposing the data into smaller series. Here symbolic-based analysis techniques that regard the dependence of data points are of some special interest. Such techniques are often prone to capacity or, on the contrary, to undersampling problems if the chosen parameters are too large. In this paper we present and apply algorithms of the relatively new ordinal symbolic approach. These algorithms use overlapping information and binary number representation, whilst being fast in the sense of algorithmic complexity, and allow, to the best of our knowledge, larger parameters than comparable methods currently used. We exploit the achieved large parameter range to investigate the limits of entropy measures based on ordinal symbolics. Moreover, we discuss data simulations from this viewpoint.

Keywords: Kolmogorov-Sinai entropy; Permutation entropy; algorithmic complexity; conditional entropy of ordinal patterns; ordinal patterns; symbolic analysis.