@article{Schöley_S29_19,
author = {Schöley, Jonas},
title={{The centered ternary balance scheme: A technique to visualize surfaces of unbalanced three-part compositions}},
journal = {Demographic Research},
volume = {S29},
number = {19},
pages = {443--458},
doi = {10.4054/DemRes.2021.44.19},
year = {2021},
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. },
URL = {https://www.demographic-research.org/special/29/19/},
eprint = {https://www.demographic-research.org/special/29/19/s29-19.pdf}
}