Visualizing Uncertainty in Sets

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 …

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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 describing 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). Following the structure of our framework, we systematically discuss basic visualization examples of integrating uncertainty in set visualizations. We draw on existing knowledge about general uncertainty visualization and previous evidence of its effectiveness.

Figures

Framework of uncertainty in set visualization with relevant set characteristics and categories of (un)certainty.

Examples of common set visualizations: (a) Euler/Venn diagrams, (b) bipartite node-link diagrams, and (c) matrices, all representing the same data.

Example dataset with certain and uncertain set memberships.

Variants of visualizing uncertain set membership in bipartite node-link diagrams and matrix representations.

Visualizing set attributes IRR (left) and AA (right) when U = 0 (top), U > 0 (middle), and U = p (bottom).

Representing uncertainty with markers indicating size variation as in (a) is not recommended for set visualizations where the area of the set does not relate to the set attribute value as in (b) and (c).

Set attributes with defined uncertainty visualized in a bipartite node-link diagram (top) and as a matrix of bar charts (bottom).

Top row (U = 0): Two courses (sets) have twenty enrolled students (elements) where all individual ages (element attribute) are known (i.e., black point symbols). Bottom row (U > 0 and U = p): Two courses (sets) have twenty enrolled students where the degree of uncertainty in student ages varies from (i) completely unknown, that is, point symbol denoted with the lightest shade of gray, to (ii) mostly unknown, (i.e., age above 30 yrs.) shown with medium gray point symbols, and to (iii) somewhat unknown (i.e., within a given age range 20-30 yrs.), assigned dark gray point symbols.

BibTeX

@article{tominski_visualizingUncertaintyInSets_2023,
 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 describing 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). Following the structure of our framework, we systematically discuss basic visualization examples of integrating uncertainty in set visualizations. We draw on existing knowledge about general uncertainty visualization and previous evidence of its effectiveness.},
 author = {Tominski, Christian and Behrisch, Michael and Bleisch, Susanne and Fabrikant, Sara Irina and Mayr, Eva and Miksch, Silvia and Purchase, Helen},
 doi = {10.1109/MCG.2023.3300441},
 journal = {IEEE Computer Graphics and Applications},
 number = {5},
 pages = {49--61},
 title = {Visualizing {Uncertainty} in {Sets}},
 url = {https://ieeexplore.ieee.org/document/10198358/},
 volume = {43},
 year = {2023}
}