Fully Three-dimensional Radial Visualization

TL;DR

This paper introduces RadViz3D, a novel method for three-dimensional radial visualization of multidimensional data, improving data representation fidelity and enabling new applications in chemistry and epidemiology.

Contribution

The paper develops a fully 3D RadViz methodology with uniform anchor point distribution, including equi-distant arrangements for Platonic solids, implemented in an R package.

Findings

RadViz3D enhances visualization fidelity for multidimensional data.

The method effectively visualizes chemical compositions and epidemiological data.

Implementation in R makes it accessible for practical use.

Abstract

We develop methodology for three-dimensional (3D) radial visualization (RadViz) of multidimensional datasets. The classical two-dimensional (2D) RadViz visualizes multivariate data in the 2D plane by mapping every observation to a point inside the unit circle. Our tool, RadViz3D, distributes anchor points uniformly on the 3D unit sphere. We show that this uniform distribution provides the best visualization with minimal artificial visual correlation for data with uncorrelated variables. However, anchor points can be placed exactly equi-distant from each other only for the five Platonic solids, so we provide equi-distant anchor points for these five settings, and approximately equi-distant anchor points via a Fibonacci grid for the other cases. Our methodology, implemented in the R package $radviz3d$, makes fully 3D RadViz possible and is shown to improve the ability of this nonlinear technique in more faithfully displaying simulated data as well as the crabs, olive oils and wine datasets. Additionally, because radial visualization is naturally suited for compositional data, we use RadViz3D to illustrate (i) the chemical composition of Longquan celadon ceramics and their Jingdezhen imitation over centuries, and (ii) US regional SARS-Cov-2 variants' prevalence in the Covid-19 pandemic during the summer 2021 surge of the Delta variant.