Conditional entropy of ordinal patterns

Anton M. Unakafov*, Karsten Keller

*Corresponding author for this work
19 Citations (Scopus)


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.

Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
Pages (from-to)94-102
Number of pages9
Publication statusPublished - 15.02.2014


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