ordpy: A Python package for data analysis with permutation entropy and ordinal network methods

Abstract

Since Bandt and Pompe’s seminal work, permutation entropy has been used in several applications and is now an essential tool for time series analysis. Beyond becoming a popular and successful technique, permutation entropy inspired a framework for mapping time series into symbolic sequences that triggered the development of many other tools, including an approach for creating networks from time series known as ordinal networks. Despite increasing popularity, the computational development of these methods is fragmented, and there were still no efforts focusing on creating a unified software package. Here, we present ordpy (http://github.com/arthurpessa/ordpy), a simple and open-source Python module that implements permutation entropy and several of the principal methods related to Bandt and Pompe’s framework to analyze time series and two-dimensional data. In particular, ordpy implements permutation entropy, Tsallis and Rényi permutation entropies, complexity–entropy plane, complexity–entropy curves, missing ordinal patterns, ordinal networks, and missing ordinal transitions for one-dimensional (time series) and two-dimensional (images) data as well as their multiscale generalizations. We review some theoretical aspects of these tools and illustrate the use of ordpy by replicating several literature results.

Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis

“…Interested readers are welcome to contact the authors for an implemented code of the PJSD in MATLAB. This method will also be available in ordpy, a Python package for data analysis with ordinal methods [90]…”

Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time series analysis

“…Interested readers are welcome to contact the authors for an implemented code of the PJSD in MATLAB. This method will also be available in ordpy, a Python package for data analysis with ordinal methods [101].…”

Determining liquid crystal properties with ordinal networks and machine learning

“…After obtaining the typical textures from the mesophases present in our samples, we average the image pixels over the three RGB layers to represent each texture as a simple array M = {y u t } u=1,...,Ny t=1,...,Nx , where y u t represents the average pixel intensity at column t and line u, while N x and N y are respectively the image width and height. We then map these two-dimensional arrays into ordinal networks [28,29]. To illustrate this method, We have made node sizes proportional to the occurring frequency of their associated ordinal patterns and used a grayscale color map to highlight edge weights (the darker the shade, the higher the weight).…”

“…We have used d x = d y = 2 in these examples and in all other results of this work, which in turn constrains our ordinal networks to have up to 24 nodes and 416 edges [28]. Furthermore, we have used the numerical implementation of ordinal networks available in the Python module ordpy [29].…”