Conditional entropy of ordinal patterns

TL;DR

This paper introduces the conditional entropy of ordinal patterns, a measure related to permutation entropy, which effectively estimates Kolmogorov-Sinai entropy and is computationally simple for analyzing complex dynamical systems.

Contribution

It defines and explores the properties of conditional entropy of ordinal patterns, demonstrating its effectiveness in estimating entropy in various dynamical systems.

Findings

Conditional entropy estimates Kolmogorov-Sinai entropy accurately.

Coincides with Kolmogorov-Sinai entropy for periodic and Markov shift systems.

Computational simplicity makes it suitable for real-world data analysis.

Abstract

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.