ComplexityMeasures.jl: scalable software to unify and accelerate entropy and complexity timeseries analysis

TL;DR

ComplexityMeasures.jl is a high-performance, open-source software that unifies and accelerates the computation of a vast array of entropy and complexity measures for time series analysis, facilitating research and application development.

Contribution

It introduces a scalable, extendable software platform with 1638 measures, optimized for performance and reliability, integrating seamlessly with nonlinear dynamics tools.

Findings

Outperforms alternative software in speed and measure coverage

Provides a reliable, modular framework for complexity analysis

Supports a large community through open-source practices

Abstract

In the nonlinear timeseries analysis literature, countless quantities have been presented as new ``entropy'' or ``complexity'' measures, often with similar roles. The ever-increasing pool of such measures makes creating a sustainable and all-encompassing software for them difficult both conceptually and pragmatically. Such a software however would be an important tool that can aid researchers make an informed decision of which measure to use and for which application, as well as accelerate novel research. Here we present {ComplexityMeasures.jl}, an easily extendable and highly performant open-source software that implements a vast selection of complexity measures. The software provides 1638 measures with 3,841 lines of source code, averaging only 2.3 lines of code per exported quantity (version 3.7). This is made possible by its mathematically rigorous composable design. In this paper we discuss the software design and demonstrate how it can accelerate complexity-related research in the future. We carefully compare it with alternative software and conclude that {ComplexityMeasures.jl} outclasses the alternatives in several objective aspects of comparison, such as computational performance, overall amount of measures, reliability, and extendability. {ComplexityMeasures.jl} is also a component of the {DynamicalSystems.jl} library for nonlinear dynamics and nonlinear timeseries analysis and follows open source development practices for creating a sustainable community of developers and contributors.