🤖 AI Summary
This study addresses the lack of effective visualization methods for grouped periodic angular data in fields such as psychology, genomics, and meteorology. The authors propose concentric circular boxplots and circular quartile plots to characterize grouped angular distributions, and further extend the approach to a three-dimensional toroidal visualization for multiple groups to reveal periodic patterns. A novel scaling strategy is introduced, wherein box width is inversely proportional to the square root of the distance from the center, enhancing visual perception. This work is the first to integrate concentric circular boxplots with toroidal 3D visualization specifically for angular data. The effectiveness and practical utility of the proposed methods are demonstrated through applications to real-world datasets, including motor resonance phases, circadian clock gene expression phases, and periodic wind direction patterns.
📝 Abstract
Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot displays of distributions of groups of angular data. The use of concentric boxplots brings challenges of visual perception, so we set the boxwidths to be inversely proportional to the square root of their distance from the centre. A perception survey supports this scaled boxwidth choice. For a large number of groups, we propose circular quartile plots. A three-dimensional toroidal display is also implemented for periodic angular distributions. We illustrate our methods on datasets in (1) psychology, to display motor resonance under different conditions, (2) genomics, to understand the distribution of peak phases for ancillary clock genes, and (3) meteorology and wind turbine power generation, to study the changing and periodic distribution of wind direction over the course of a year.