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Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

Micallef, Luana (2013) Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams. Doctor of Philosophy (PhD) thesis, University of Kent. (KAR id:47958)

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Abstract

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams.

This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Rodgers, Peter
Additional information: Revised version approved February 2015; Highly commended as a runner-up in the 2016 BCS/CHPC Distinguished Dissertation award
Uncontrolled keywords: set visualization Venn diagram Euler diagram set relations set cardinalities information visualization
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Luana Micallef
Date Deposited: 13 Apr 2015 10:01 UTC
Last Modified: 16 Feb 2021 13:24 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/47958 (The current URI for this page, for reference purposes)
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