Volume 44 - Article 19 | Pages 443–458 Author has provided data and code for replicating results

The centered ternary balance scheme: A technique to visualize surfaces of unbalanced three-part compositions

By Jonas Schöley

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Date received:15 Mar 2019
Date published:09 Mar 2021
Word count:2000
Keywords:compositional data, data visualization, multidimensional color scales
Additional files:readme.44-19 (text file, 23 kB)
 demographic-research.44-19 (zip file, 4 MB)
Weblink:You will find all publications in this Special Collection on Data Visualization here.


Background: The ternary balance scheme is a visualization technique that encodes three-part compositions as a mixture of three primary colors. The technique works best if the compositional data are well spread out across the domain but fails to show structure in very unbalanced data.

Objective: I extend the ternary balance scheme such that it can be utilized to show variation in unbalanced compositional surfaces.

Methods: By reprojecting an unbalanced compositional data set around its center of location and visualizing the transformed data with a standard ternary balance scheme, the internal variation of the data becomes visible. An appropriate centering operation has been defined within the field of compositional data analysis.

Results: Using Europe’s regional workforce structure by economic sector as an example, I have demonstrated the utility of the centered ternary balance scheme in visualizing variation across unbalanced compositional surfaces.

Contribution: I have proposed a technique to visualize the internal variation in surfaces of highly unbalanced compositional data and implemented it in the tricolore R package.

Author's Affiliation

Jonas Schöley - Syddansk Universitet, Denmark [Email]

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