Fully Three-dimensional Radial Visualization

We develop methodology for three-dimensional (3D) radial visualization (RadViz) of multidimensional datasets. 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. Graphical display of multivariate data is important to obtain insight into their properties and similarity or distinctiveness of different groups [1].