Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of domain points. We propose the embedding of adaptive correlation sampling into chord diagrams with hierarchical edge bundling to alleviate these constraints. Entities representing spatial regions are arranged along the circular chord layout via a space-filling curve, and Bayesian optimal sampling is used to efficiently estimate the maximum occurring correlation between any two points from different regions. Hierarchical edge bundling reduces visual clutter and emphasizes the major correlation structures. By selecting an edge, the user triggers a focus diagram in which only the two regions connected via this edge are refined and arranged in a specific way in a second chord layout. For visualizing correlations between two different variables, which are not symmetric anymore, we switch to showing a full correlation matrix. This avoids drawing the same edges twice with different correlation values. We introduce GPU implementations of both linear and non-linear correlation measures to further reduce the time that is required to generate the context and focus views, and to even enable the analysis of correlations in a 1000-member ensemble.

翻译：可视化三维集合中的空间相关性因需传达海量信息而极具挑战性。内存与时间约束使得预计算并存储所有域点对间的相关性不可行。我们提出将自适应相关性采样嵌入具有层次边捆绑的弦图以缓解这些约束。表示空间区域的实体通过空间填充曲线沿圆形弦图布局排列，并采用贝叶斯最优采样高效估计不同区域任意两点间出现的最大相关性。层次边捆绑可减少视觉混乱并突出主要相关结构。通过选择某条边，用户可触发一个聚焦视图，其中仅对该边连接的两个区域进行细化处理，并以特定方式排列于第二个弦图中。当可视化两个非对称变量间的相关性时，我们切换至显示完整相关性矩阵，从而避免以不同相关性值重复绘制同一条边。我们引入线性和非线性相关性度量的GPU实现，进一步减少生成上下文与聚焦视图所需时间，甚至支持对含1000个成员集合的相关性分析。