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.©2013 Elsevier B.V. All rights reserved.
Unakafov, A. M., & Keller, K. (2014). Conditional entropy of ordinal patterns. Physica D: Nonlinear Phenomena, 269, 94–102. https://doi.org/10.1016/j.physd.2013.11.015