CSDL Home IEEE Transactions on Visualization & Computer Graphics 2010 vol.16 Issue No.06 - November/December

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Issue No.06 - November/December (2010 vol.16)

pp: 1090-1099

Nathalie Henry Riche , Microsoft Research

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.210

ABSTRACT

In many common data analysis scenarios the data elements are logically grouped into sets. Venn and Euler style diagrams are a common visual representation of such set membership where the data elements are represented by labels or glyphs and sets are indicated by boundaries surrounding their members. Generating such diagrams automatically such that set regions do not intersect unless the corresponding sets have a non-empty intersection is a difficult problem. Further, it may be impossible in some cases if regions are required to be continuous and convex. Several approaches exist to draw such set regions using more complex shapes, however, the resulting diagrams can be difficult to interpret. In this paper we present two novel approaches for simplifying a complex collection of intersecting sets into a strict hierarchy that can be more easily automatically arranged and drawn (Figure 1). In the first approach, we use compact rectangular shapes for drawing each set, attempting to improve the readability of the set intersections. In the second approach, we avoid drawing intersecting set regions by duplicating elements belonging to multiple sets. We compared both of our techniques to the traditional non-convex region technique using five readability tasks. Our results show that the compact rectangular shapes technique was often preferred by experimental subjects even though the use of duplications dramatically improves the accuracy and performance time for most of our tasks. In addition to general set representation our techniques are also applicable to visualization of networks with intersecting clusters of nodes

INDEX TERMS

Information Visualization, Euler diagrams, Set Visualization, Graph Visualization.

CITATION

Nathalie Henry Riche, "Untangling Euler Diagrams",

*IEEE Transactions on Visualization & Computer Graphics*, vol.16, no. 6, pp. 1090-1099, November/December 2010, doi:10.1109/TVCG.2010.210REFERENCES

- [1] J. Abello, F. van Ham, and N. Krishnan, Ask-graphview: A large scale graph visualization system.
IEEE Transactions on Visualization and Computer Graphics, 12: 669–676, 2006.- [2] B. B. Bederson, B. Shneiderman, and M. Wattenberg, Ordered and quantum treemaps: Making effective use of 2d space to display hierarchies.
ACM Trans. Graph., 21 (4): 833–854, October 2002.- [3] F. Benoy and P. Rodgers, Evaluating the comprehension of euler diagrams.
In IEEE IV, pages 771–780, 2007.- [4] A. F. Blackwell, K. Marriott, and A. Shimojima editors.
, Diagrammatic Representation and Inference, Third International Conference, Diagrams 2004,Cambridge, UK, March 22–24, 2004, Proceedings, volume 2980 of Lecture Notes in Computer Science. Springer, 2004.- [5] S. Chow http://webhome.cs.uvic.ca/schow.
- [6] S. Chow,
Generating and drawing area-proportional euler and venn diagrams. PhD thesis, University of Victoria, Canada, 2007.- [7] C. Collins, G. Penn, and S. Carpendale, Bubble sets: Revealing set relations with isocontours over existing visualizations.
IEEE TVCG, 15: 1009–1016, 2009.- [8] T. Dwyer, Y. Koren, and K. Marriott, Ipsep-cola: An incremental procedure for separation constraint layout of graphs.
IEEE TVCG, 12: 821–828, 2006.- [9] T. Dwyer, K. Marriott, F. Schreiber, P. Stuckey, M. Woodward, and M. Wybrow, Exploration of networks using overview+detail with constraint-based cooperative layout.
IEEE TVCG, 14 (6): 1293–1300, 2008.- [10] T. Dwyer, K. Marriott, and P. J. Stuckey, Fast node overlap removal.
In Proc. 13th Intl. Symp. Graph Drawing(GD'05), volume 3843 of LNCS, pages 153–164. Springer, 2006.- [11] P. Eades and Q.-W. Feng, Multilevel visualization of clustered graphs.
In Proc. Graph Drawing, GD, number 1190 in LNCS, pages 101–112, Berlin, Germany, 1996. Springer-Verlag. - [12] N. Elmqvist, P. Dragicevic, and J.-D. Fekete, Rolling the dice: Multidimensional visual exploration using scatterplot matrix navigation.
IEEE TVCG, 14 (6): 1141–1148, 2008.- [13] A. Fish and G. Stapleton, Defining euler diagrams: choices and consequences.
Euler Diagrams Workshop, 2005.- [14] J. Flower and J. Howse, Generating euler diagrams.
In DIAGRAMS `02: Proc. of the 2nd International Conference on Diagrammatic Representation and Inference, pages 61–75. Springer-Verlag, 2002.- [15] W. Freiler, K. Matkovic, and H. Hauser, Interactive visual analysis of set-typed data.
IEEE TVCG, 14 (6): 1340–1347, 2008.- [16] E. M. Hammer,
Logic and Visual Information. CSLI Publications, 1995.- [17] J. Heer and D. Boyd, Vizster: Visualizing online social networks.
In Proc. Intl. Symp. Information Visualization (Infovis'05). IEEE, 2005.- [18] N. Henry, A. Bezerianos, and J.-D. Fekete, Improving the readability of clustered social networks using node duplication.
IEEE TVCG, 14 (6): 1317–1324, 2008.- [19] N. Henry, J.-D. Fekete, and M. J. McGuffin, NodeTrix: a hybrid visualization of social networks.
IEEE TVCG, 13 (6): 1302–1309, 2007.- [20] N. Henry-Riche and T. Dwyer, Untangling euler diagrams.
Technical Report, 2010. http://research.microsoft.com/nathEulerDiagrams. - [21] J. Howse, F. Molina, J. Taylor, S. Kent, and J. Gil, Spider diagrams: A diagrammatic reasoning system.
Journal of Visual Languages and Computing, 12 (3): 299–324, 2001.- [22] A. K. Jain, M. N. Murty, and P. J. Flynn, Data clustering: a review.
ACM Comput. Surv., 31 (3): 264–323, 1999.- [23] G. Kanizsa and W. Gerbino, Convexity and symmetry in figure-ground organization. In M. H. ed., editor,
, Vision and artifact. M. Henle ed., New York: Springer, 1976.- [24] H. Kestler, A. Muller, J. Kraus, M. Buchholz, T. Gress, H. Liu, D. Kane, B. Zeeberg, and J. Weinstein, Vennmaster: Area-proportional euler diagrams for functional go analysis of microarrays.
BMC Bioinformatics, 9 (1), 2008.- [25] B. H. Kim, B. Lee, and J. Seo, Visualizing set concordance with permutation matrices and fan diagrams.
Interacting with Computers, 19 (5–6): 630–643, 2007.- [26] P.-Y. Koenig, G. Melancon, C. Bohan, and B. Gautier, Combining dagmaps and sugiyama layout for the navigation of hierarchical data.
IEEE IV, 0: 447–452, 2007.- [27] K. Koffka,
Principles of Gestaltpsychology. Oxford, England: Harcourt, Brace, 1935.- [28] Z. Liu, D. W. Jacobs, and R. Basri, The role of convexity in perceptual completion: beyond good continuation.
Vision Research, 39 (25): 4244–4257, 1999.- [29] G. Palla, I. Derenyi, I. Farkas, and T. Vicsek, Uncovering the overlapping community structure of complex networks in nature and society.
Nature, 435 (7043): 814–818, June 2005.- [30] B. Shneiderman and A. Aris, Network visualization by semantic substrates.
IEEE TVCG, 12: 733–740, 2006.- [31] P. Simonetto, D. Auber, and D. Archambault, Fully automatic visualisation of overlapping sets.
Comput. Graph. Forum, 28 (3): 967–974, 2009.- [32] A. Spoerri, Infocrystal: a visual tool for information retrieval.
In VIS'93: Proceedings of the 4th conference on Visualization'93, pages 150–157, Washington, DC, USA, 1993. IEEE Computer Society. - [33] A. Verroust and M.-L. Viaud, Ensuring the drawability of extended euler diagrams for up to 8 sets.
In LNAI2980, pages 128–141, 2003. |