Measuring and Interpreting the Quality of 3D Projections of High-Dimensional Data

Projections of high-dimensional data are among the most frequently used tools for exploring such data in information visualization. In contrast to 2D projections, which create static planar scatterplots, 3D projections create point clouds that can be visually explored from many viewpoints. The relative added value of using 3D projections is still a topic for debate in the community, having both proponents and critics. In this work, we propose several techniques to both increase the effectiveness of exploration of 3D projections and also measure their quality. We start by extending well-known definitions of 2D projection quality metrics to account for user-chosen viewpoints and inherent occlusion of 3D projections when viewed from such viewpoints. We also propose an interactive exploration tool for finding high-quality viewpoints from the perspective of such metrics. Using our tool, we show that 3D projections often allow viewpoints exhibiting higher quality than their 2D counterparts. Next, we enrich the interpretation of such viewpoints by explanatory techniques for 2D projections and show that good viewpoints, from the perspective of our metrics, also allow easy-to-interpret explanations of the depicted data. We use our tool in a user study to gauge how our computed quality metrics correlate with user-perceived quality for a cluster identification task. Our results show that our metrics can predict well viewpoints deemed good by users and that our tool increases the users’ preference for 3D projections as compared to classical 2D projections.