Visualizing Uncertainty in Sets

TL;DR

This paper tackles the challenge of visualizing uncertainty in set-type data by proposing a formal framework that links set data facets ($D$: set membership, set attributes, element attributes) with uncertainty types ($U$: $U=0$, $U>0$, $U=p$). It situates set visualization within the broader uncertainty-visualization literature, adopting a pipeline view $(D,U) \to V \to (D',U')$ and leveraging MacEachren's guidelines to inform visual-variable choices. The authors classify the design space into areas with existing methods (green) and gaps (orange), and provide concrete visualization strategies for uncertain membership, set attributes, and element attributes using explicit representations (bipartite diagrams, matrices) and augmentations (texture, color, edges). They discuss practical challenges such as clutter, task specificity, and evaluation, offering design recommendations and outlining open questions around uncertainty propagation, temporal/spatial aspects, and missing vs uncertain data. Overall, the work advances understanding of how to communicate both set data and their uncertainty, and identifies concrete directions for future research to improve expressive, usable uncertainty-in-sets visualizations.

Abstract

Set visualization facilitates the exploration and analysis of set-type data. However, how sets should be visualized when the data is uncertain is still an open research challenge. To address the problem of depicting uncertainty in set visualization, we ask (i) which aspects of set type data can be affected by uncertainty and (ii) which characteristics of uncertainty influence the visualization design. We answer these research questions by first developing a conceptual framework that brings together (i) the information that is primarily relevant in sets (i.e., set membership, set attributes, and element attributes) and (ii) different plausible categories of (un)certainty (i.e., certainty, undefined uncertainty as a binary fact, and defined uncertainty as quantifiable measure). Based on the conceptual framework, we systematically discuss visualization examples of integrating uncertainty in set visualizations. We draw on existing knowledge about general uncertainty visualization and fill gaps where set-specific aspects have not yet been considered sufficiently.

Figures (15)

• Figure 1: Common visual representations of sets include Euler/Venn diagrams (a), bipartite node-link diagrams (b), and matrices (c), all representing the same data.
• Figure 2: Prior work on visualizing defined uncertainty and set membership in (a) Venn diagrams Zhu2018 and (b) node-link diagrams Vehlow2013 as well as visualizing uncertainty and set size in (c) treemaps Sondag2020 and (d) with circle packing Goertler2018.
• Figure 3: Example data for sets memberships.
• Figure 4: Variants of visualizing uncertain set membership in bipartite node-link diagrams.
• Figure 5: Variants of visualizing uncertain set membership in matrix representations.