Area-proportional Visualization for Circular Data

Data visualization is important for statistical analysis, as it helps convey information efficiently and shed lights on the hidden patterns behind data in a visual context. It is particularly helpful to display circular data in a 2-dimensional space to accommodate its non-linear support space and reveal the underlying circular structure which is otherwise not obvious in 1-dimension. In this paper, we first formally categorize circular plots into two types, either height- or area-proportional, and then describe a new general methodology that can be used to produce circular plots, particularly in the area-proportional manner, which in our opinion is the more appropriate choice. Formulae are given that are fairly simple yet effective to produce various circular plots, such as smooth density curves, histograms, rose diagrams, dot plots, and plots for multi-class data.数据可视化之于统计分析至关重要，它既能高效传递信息，又可在可视化语境下揭示数据背后潜藏的模式。针对圆形数据（circular data），在二维空间中进行可视化尤为实用：既可以适配其非线性支撑空间，又能揭示其内在的圆形结构——这类结构在一维空间中往往难以被察觉。本文首先将圆形图（circular plots）正式划分为两类：高度比例型与面积比例型；随后提出一种全新的通用方法，可用于生成各类圆形图，尤其擅长生成面积比例型圆形图——我们认为后者是更为合适的选择。本文给出了简洁高效的公式，可用于生成各类圆形图，包括平滑密度曲线、直方图（histograms）、玫瑰图（rose diagrams）、点图（dot plots）以及多分类数据可视化图。