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：在三维集合中可视化空间相关性极具挑战性，因为需要传达海量信息。受限于内存和时间约束，预计算并存储所有域点对之间的相关性是不可行的。我们提出将自适应相关性采样嵌入带有层次边缘绑定技术的弦图中，以缓解这些约束。代表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之间出现的最大相关性。层次边缘绑定减少了视觉杂乱，并突出主要的相关结构。通过选择一条边，用户可触发一个焦点图，其中仅通过该边连接的两个区域被细化并以特定方式排列在第二个弦图中。对于不再具有对称性的两个不同变量间的相关性可视化，我们切换为展示完整相关矩阵，以避免使用不同相关性值重复绘制同一条边。我们引入了线性和非线性相关性度量的GPU实现，以进一步减少生成上下文和焦点视图所需的时间，从而甚至能够分析包含1000个成员集合中的相关性。