Explaining three-dimensional dimensionality reduction plots

Understanding three-dimensional projections created by dimensionality reduction from high-variate datasets is very challenging. In particular, classical three-dimensional scatterplots used to display such projections do not explicitly show the relations between the projected points, the viewpoint used to visualize the projection, and the original data variables. To explore and explain such relations, we propose a set of interactive visualization techniques. First, we adapt and enhance biplots to show the data variables in the projected threedimensional space. Next, we use a set of interactive bar chart legends to show variables that are visible from a given viewpoint and also assist users to select an optimal viewpoint to examine a desired set of variables. Finally, we propose an interactive viewpoint legend that provides an overview of the information visible in a given three-dimensional projection from all possible viewpoints. Our techniques are simple to implement and can be applied to any dimensionality reduction technique. We demonstrate our techniques on the exploration of several real-world high-dimensional datasets.