Visual Entropy and the Visualization of Uncertainty. Holliman, N. S.; Coltekin, A.; Fernstad, S. J.; Simpson, M. D.; Wilson, K. J.; and Woods, A. J. arXiv:1907.12879 [cs, math], July, 2019. ZSCC: 0000002 arXiv: 1907.12879
Visual Entropy and the Visualization of Uncertainty [link]Paper  abstract   bibtex   
Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 \textgreater0.97, p\textless0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.
@article{holliman_visual_2019,
	title = {Visual {Entropy} and the {Visualization} of {Uncertainty}},
	url = {http://arxiv.org/abs/1907.12879},
	abstract = {Background: It is possible to find many different visual representations of data values in visualizations, it is less common to see visual representations that include uncertainty, especially in visualizations intended for non-technical audiences. Objective: our aim is to rigorously define and evaluate the novel use of visual entropy as a measure of shape that allows us to construct an ordered scale of glyphs for use in representing both uncertainty and value in 2D and 3D environments. Method: We use sample entropy as a numerical measure of visual entropy to construct a set of glyphs using R and Blender which vary in their complexity. Results: A Bradley-Terry analysis of a pairwise comparison of the glyphs shows participants (n=19) ordered the glyphs as predicted by the visual entropy score (linear regression R2 {\textgreater}0.97, p{\textless}0.001). We also evaluate whether the glyphs can effectively represent uncertainty using a signal detection method, participants (n=15) were able to search for glyphs representing uncertainty with high sensitivity and low error rates. Conclusion: visual entropy is a novel cue for representing ordered data and provides a channel that allows the uncertainty of a measure to be presented alongside its mean value.},
	urldate = {2020-10-14},
	journal = {arXiv:1907.12879 [cs, math]},
	author = {Holliman, Nicolas S. and Coltekin, Arzu and Fernstad, Sara J. and Simpson, Michael D. and Wilson, Kevin J. and Woods, Andrew J.},
	month = jul,
	year = {2019},
	note = {ZSCC: 0000002 
arXiv: 1907.12879},
	keywords = {Computer Science - Graphics, Computer Science - Human-Computer Interaction, Computer Science - Information Theory},
}
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