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

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.