This Article 
 Bibliographic References 
 Add to: 
Wellformedness Properties in Euler Diagrams: Which Should Be Used?
July 2012 (vol. 18 no. 7)
pp. 1089-1100
Leishi Zhang, Fachbereich Inf. und Informationswissenschaft, Univ. Konstanz, Konstanz, Germany
P. Rodgers, Sch. of Comput., Univ. of Kent, Canterbury, UK
H. Purchase, Sch. of Comput. Sci., Univ. of Glasgow, Glasgow, UK
Euler diagrams are often used to visualize intersecting data sets in applications such as criminology; genetics, medicine, and computer file systems. One interesting aspect of these diagrams is that some data sets cannot be drawn without breaking one or more "wellformedness properties,” which are considered to reduce the user comprehension of the diagrams. However, it is possible to draw the same data with different diagrams, each of which breaks different wellformedness properties. Hence, some properties are "swappable,” so motivating the study of which of the alternatives would be best to use. This paper reports on the two empirical studies to determine how wellformedness properties affect comprehension. One study was with abstract data, the other was with concrete data that visualized students' enrollment on university modules. We have results from both studies that imply that diagrams with concurrency or disconnected zones perform less well than other some other properties. Further, we have no results that imply that diagrams with brushing points adversely affect performance. Our data also indicate that nonsimple curves are preferred less than diagrams with other properties. These results will inform both human diagram designers and the developers of automated drawing systems on the best way to visualize data using Euler diagrams.

[1] J. Barwise and A. Shimojima, “Surrogate Reasoning,” Cognitive Studies: Bull. of Japanese Cognitive Science Soc., vol. 2, no. 4, pp. 7-26, 1995.
[2] F. Benoy and P. Rodgers, “Evaluating the Comprehension of Euler Diagrams,” Proc. 11th Int'l Conf. Information Visualization (IV '07), pp. 771-778, July 2007.
[3] S. Chow, “Generating and Drawing Area-Proportional Venn and Euler Diagrams,” PhD thesis, Univ. of Victoria, 2008.
[4] S. Chow and F. Ruskey, “Drawing Area-Proportional Venn and Euler Diagrams,” Proc. Graph Drawing, pp. 466-477, 2003.
[5] R. DeChiara, U. Erra, and V. Scarano, “VennFS: A Venn Diagram File Manager,” Proc. Seventh Int'l Conf. Information Visualization (IV '03), pp. 120-126, 2003.
[6] L. Euler, “Lettres à une Princesse d'Allemagne,” vol 2., Letters nos. 102-108, 1761.
[7] G. Farfel and W. Sousa, “Repeat Victimization and Hot Spots: The Overlap and Its Implication for Crime Control and Problem-Oriented Policing,” Crime Prevention Studies vol. 12, pp. 221-240, 2001.
[8] A. Fish, B. Khazaei, and C. Roast, “Exploring Human Factors in Formal Diagram Usage,” Engineering Interactive Systems, pp. 413-428, Springer-Verlag, 2007.
[9] A. Fish, B. Khazaei, and C. Roast, “User-Comprehension of Euler Diagrams,” J. Visual Languages and Computing, vol. 22, no. 5, pp. 340-354, 2011, doi:10.1016/j.jvlc2011.01.002.
[10] J. Flower and J. Howse, “Generating Euler Diagrams,” Proc. Second Int'l Conf. Diagrammatic Representation and Inference (Diagrams), pp. 61-75, 2002.
[11] S. Hughes, “The Great British Venn Diagram,” http://qntm.orguk, June 2011.
[12] H. Kestler, A. Muller, T. Gress, and M. Buchholz, “Generalized Venn Diagrams: A New Method for Visualizing Complex Genetic Set Relations,” J. Bioinformatics, vol. 21, no. 8, pp. 1592-1595, 2005.
[13] N.H. Riche and T. Dwyer, “Untangling Euler Diagrams,” IEEE Trans. Visualization and Computer Graphics, vol. 16, no. 6, pp. 1090-1099, Nov./Dec. 2010.
[14] P. Rodgers, J. Howse, G. Stapleton, and L. Zhang, “Euler Graph Transformations for Euler Diagram Layout,” Proc. IEEE Symp. Visual Languages and Human Centric Computing (VL/HCC '10), pp. 111-118, Sept. 2010.
[15] P. Rodgers, L. Zhang, and A. Fish, “General Euler Diagram Generation,” Proc. Int'l Conf. Diagrammatic Representation and Inference (Diagrams), pp. 13-27, 2008.
[16] P. Simonetto, D. Auber, and D. Archambault, “Fully Automatic Visualisation of Overlapping Sets,” Computer Graphics Forum, vol. 28, no. 3, pp. 967-974, 2009.
[17] J. Soriano, K. Davis, B. Coleman, G. Visick, D. Mannino, and N. Pride, “The Proportional Venn Diagram of Obstructive Lung Disease: Two Approximations from the United States and the United Kingdom,” Chest, vol. 124, pp. 474-481, 2003.
[18] G. Stapleton, P. Rodgers, J. Howse, and J. Taylor, “Properties of Euler Diagrams,” Proc. Workshop Layout of (Software) Eng. Diagrams, 2007.
[19] A. Treismana and J. Southera, “Search Asymmetry: A Diagnostic for Preattentive Processing of Separable Features,” J. Experimental Psychology: General, vol. 114, no. 3, pp. 285-310, Sept. 1985.
[20] J. Venn, “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings,” Philosophical Magazine, vol. 5, no. 9, pp. 1-18, 1880.
[21] A. Verroust and M.-L. Viaud, “Ensuring the Drawability of Euler Diagrams for Up to Eight Sets,” Proc. Third Int'l Conf. Theory and Application of Diagrams, pp. 128-141, 2004.
[22] C. Ziemkiewicz and R. Kosara, “Beyond Bertin: Seeing the Forest despite the Trees,” IEEE Computer Graphics and Applications, vol. 30, no. 5, pp. 7-11, Sept./Oct. 2010.

Index Terms:
data visualisation,automated drawing systems,wellformedness properties,Euler diagrams,intersecting data sets visualization,criminology,genetics,medicine,computer file systems,comprehension,student enrollment visualization,university modules,brushing points,human diagram designers,Handheld computers,Decision support systems,information visualization.,Euler diagrams,Venn diagrams,empirical studies
Leishi Zhang, P. Rodgers, H. Purchase, "Wellformedness Properties in Euler Diagrams: Which Should Be Used?," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 7, pp. 1089-1100, July 2012, doi:10.1109/TVCG.2011.143
Usage of this product signifies your acceptance of the Terms of Use.