Computing Science Algorithmic data analysis track Master’s Thesis A VIEWPOINT-DRIVEN COMPARISON OF 3D VERSUS 2D PROJECTIONS OF HIGH-DIMENSIONAL DATA

Dimensionality reduction is a popular data visualization technique that projects high-dimensional data to a low-dimensional space (2D or 3D) while preserving distance and/or neighborhood relations between points. The projected dataset can then be visualized in, for example, a scatterplot. This process greatly enhances interpretability of the dataset while minimizing information loss. While projections that target the 2D space have been studied in detail both quantitatively and qualitatively, 3D projections are far less well understood, with authors arguing both for and against the added value of a third visual dimension. More information can be stored in 3 dimensions, and point overlap in visualizations is reduced, but exploring and understanding a 3D projection adds complexity for users. A user can only ever see a 2D rendering of the 3D projection as seen from a certain viewpoint. In each view many points can be occluded, and therefore, in order to assess the entire projection, it is required to consider multiple views found by rotating it. Certain quality metrics can measure to what extent the structure of a dataset is preserved in a projection. But as of now, quantitative studies of 3D projections have disregarded this viewpoint limitation in 3D by using quality metrics that consider point neighborhoods and inter-point distances in 3D. We propose a different approach of measuring the quality of 3D projections, where we use quality metrics designed for 2D projections not on the entire 3D projection, but on multiple 2D views of a 3D projection. This tells us how the quality of a 3D projection changes as a function of the viewpoint, which we believe can give a better answer to the question of when and why 3D projections have added value over 2D projections from a user perspective. After a quantitative analysis of 30 3D projections we find that generally, most views of a 3D projection are of relatively high quality, with only a few considerably worse views. Therefore, users should not have trouble finding one of the better views. We furthermore find that, depending on the projection technique and chosen quality metric, many single views of a 3D projection can have higher quality than a 2D projection made with the same projection technique. We perform a user study to gain more insight in how users perceive the quality of single views of a 3D projection, and whether standard quality metrics can predict whether users will deem a view to be of good quality. Most importantly, we find that the strength of the correlation between measured quality of a viewpoint and user perceived quality depends on which dataset is projected. In some cases there appears to be no correlation at all. For projections where this correlation is strong, we observe an increased benefit of using a tool that suggests high quality viewpoints to users. In general, we find that in terms of user perceived quality, a 3D projection is just as good as or better than a 2D projection generated by the same projection technique. Furthermore, we find that users believe 3D projections to better display the dataset structure than their 2D counterpart.