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

Jonas Schöley

doi:10.4054/DemRes.2021.44.19

Volume 44 - Article 19 | Pages 443–458

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

By Jonas Schöley

Date received:

15 Mar 2019

Date published:

9 Mar 2021

Word count:

2000

Keywords:

compositional data, data visualization, multidimensional color scales

DOI:

10.4054/DemRes.2021.44.19

Replicable Material:

demographic-research.44-19 (zip file, 4 MB)
readme.44-19 (text file, 23 kB)

This article is part of the Special Collection 29 "Data Visualization"

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Abstract

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.