Three-dimensional Radial Visualization of High-dimensional Datasets with Mixed Features

We develop methodology for 3D radial visualization (RadViz) of high-dimensional datasets. Our display engine is called RadViz3D and extends the classical 2D RadViz that visualizes multivariate data in the 2D plane by mapping every record to a point inside the unit circle. We show that distributing anchor points at least approximately uniformly on the 3D unit sphere provides a better visualization with minimal artificial visual correlation for data with uncorrelated variables. Our RadViz3D methodology therefore places equi-spaced anchor points, one for every feature, exactly for the five Platonic solids, and approximately via a Fibonacci grid for the other cases. Our Max-Ratio Projection (MRP) method then utilizes the group information in high dimensions to provide distinctive lower-dimensional projections that are then displayed using Radviz3D. Our methodology is extended to datasets with discrete and continuous features where a Gaussianized distributional transform is used in conjunction with copula models before applying MRP and visualizing the result using RadViz3D. A R package radviz3d implementing our complete methodology is available.