Allotaxonometry and rank-turbulence divergence: A universal instrument for comparing complex systems

TL;DR

The paper introduces allotaxonometry and rank-turbulence divergence, innovative tools for comparing complex systems with diverse components, demonstrated across various real-world datasets to reveal insightful differences.

Contribution

It develops a universal, tunable rank-based divergence method and a visual allotaxonograph for analyzing and comparing complex systems' component distributions.

Findings

Effective comparison of diverse complex systems demonstrated

Rank-turbulence divergence reveals meaningful differences in datasets

Tools are adaptable across multiple domains

Abstract

Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce `allotaxonometry' along with `rank-turbulence divergence' (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram for rank-rank pairs with an ordered list of components according to divergence contribution. We explore the performance of rank-turbulence divergence, which we view as an instrument of `type calculus', for a series of distinct settings including: Language use on Twitter and in books, species abundance, baby name popularity, market capitalization, performance in sports, mortality causes, and job titles. We provide a series of supplementary flipbooks which demonstrate the tunability and storytelling power of rank-based allotaxonometry.