Clutter Reduction in Multi-dimensional Visualization of Incomplete Data Using Sugiyama Algorithm

Visualization of uncertainty in datasets is a new field of research, which aims to represent incomplete data for analysis in real scenarios. In many cases, datasets, especially multi-dimensional datasets, often contain either errors or uncertain values. To address this challenge, we may treat these uncertainties as scalar values like probability. For visual representation in parallel coordinates, we draw a small "circle" to temporarily define a dummy vertex for an uncertain value of a data item, at the crossing point between polylines and the axis of certain dimension. Furthermore, these temporary positions of uncertainty could be permuted to achieve visual effectiveness. This feature provides a great opportunity by optimizing the order of uncertain values to tackle another important challenge in information visualization: clutter reduction. Visual clutter always obscures the visualizing structure even in small datasets. In this paper, we apply Sugiyama's layered directed graph drawing algorithm into parallel coordinates visualization to minimize the number of edge crossing among polylines, which has significantly improved the readability of visual structure. Experiments in case studies have shown the effectiveness of our new methods for clutter reduction in parallel coordinates visualization. These experiments also imply that besides visual clutter, the number of uncertain values and the type of multi-dimensional data are important attributes that affect visualization performance in this field.