Sclow Plots: Visualizing Empty Space

Abstract

Scatter plots are mostly used for correlation analysis, but are also a useful tool for understanding the distribution of highdimensional point cloud data. An important characteristic of such distributions are clusters, and scatter plots have been used successfully to identify clusters in data. Another characteristic of point cloud data that has received less attention so far are regions that contain no or only very few data points. We show that augmenting scatter plots by projections of flow lines along the gradient vector field of the distance function to the point cloud reveals such empty regions or voids. The augmented scatter plots, that we call sclow plots, enable a much better understanding of the geometry underlying the point cloud than traditional scatter plots, and by that support tasks like dimension inference, detecting outliers, or identifying data points at the interface between clusters. We demonstrate the feasibility of our approach on synthetic and real world data sets.