Abstract
In this paper we address the problem of visualizing overlapping sets of points with a fixed positioning in a comprehensible way. A standard visualization technique is to enclose the point sets in isocontours generated by bounding a potential field function. The most commonly used functions are various approximations of the Gaussian distribution. Such an approach produces smooth and appealing shapes, however it may produce an incorrect point nesting in generated regions, e.g. some point is contained inside a foreign set region. We introduce a different potential field function that keeps the desired properties of Gaussian distribution, and in addition guarantees that every point belongs to all its sets’ regions and no others, and that regions of two sets with no common points have no overlaps.
The presented function works well if the sets intersect each other, a situation that often arises in social network graphs, producing regions that reveal the structure of their clustering. It performs best when the graphs are positioned by force-directed layout algorithms. The function can also be used to depict hierarchical clustering of the graphs. We study the performance of the method on various real-world graph examples.
Supported by ERAF project 2010/0318/2DP/2.1.1.1.0/10/APIA/VIAA/104.
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References
Balzer, M., Deussen, O.: Level-of-detail visualization of clustered graph layouts. In: 2007 6th International AsiaPacific Symposium on Visualization, pp. 133–140 (2007)
Blinn, J.F.: A generalization of algebraic surface drawing. ACM Trans. Graph. 1(3), 235–256 (1982)
Byelas, H., Telea, A.: Towards realism in drawing areas of interest on architecture diagrams. J. Vis. Lang. Comput. 20(2), 110–128 (2009)
Collins, C., Penn, G., Carpendale, S.: Bubble sets: revealing set relations with isocontours over existing visualizations. IEEE Trans. Vis. Comput. Graph. 15(6), 1009–1016 (2009)
Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall PTR, Upper Saddle River (1998)
Dinkla, K., van Kreveld, M.J., Speckmann, B., Westenberg, M.A.: Kelp diagrams: point set membership visualization. Comput. Graph. Forum 31(3pt1), 875–884 (2012)
Douglas, D.H., Peucker, T.K.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica Int. J. Geogr. Inf. Geovisualization 10(2), 112–122 (1973)
Gansner, E.R., Hu, Y., Kobourov, S.: GMap: Visualizing graphs and clusters as maps. In: 2010 IEEE Pacific Visualization Symposium PacificVis, pp. 201–208 (2010)
Goh, K.-I., Cusick, M.E., Valle, D., Childs, B., Vidal, M., Barabsi, A.-L.: The human disease network. Proc. Natl. Acad. Sci. USA 104(21), 8685–8690 (2007)
Gross, M.H., Sprenger, T.C., Finger, J.: Visualizing information on a sphere. In: Proceedings of the 1997 Conference on Information Visualization, pp. 11–16 (1997)
Heer, J., Boyd, D.: Vizster: visualizing online social networks. In: IEEE Symposium on Information Visualization 2005 INFOVIS 2005, vol. 5, pp. 32–39 (2003)
Hobby, J.D.: Smooth, easy to compute interpolating splines. Discrete Comput. Geom. 1(2), 123–140 (1986)
Krebs, V.: Managing the 21st century organization. IHRIM J. XI(4), 2–8 (2007)
Matsumoto, Y., Umano, M., Inuiguchi, M.: Visualization with Voronoi tessellation and moving output units in self-organizing map of the real-number system. Neural Netw. 1, 3428–3434 (2008)
Riche, N.H., Dwyer, T.: Untangling Euler diagrams. IEEE Trans. Vis. Comput. Graph. 16(6), 1090–1099 (2010)
Rosenthal, P., Linsen, L.: Enclosing surfaces for point clusters using 3D discrete Voronoi diagrams. Comput. Graph. Forum 28(3), 999–1006 (2009)
Santamaría, R., Therón, R.: Overlapping clustered graphs: co-authorship networks visualization. In: Butz, A., Fisher, B., Krüger, A., Olivier, P., Christie, M. (eds.) SG 2008. LNCS, vol. 5166, pp. 190–199. Springer, Heidelberg (2008)
Simonetto, P., Auber, D., Archambault, D.: Fully automatic visualisation of overlapping sets. Comput. Graph. Forum 28(3), 967–974 (2009)
Sprenger, T.C., Brunella, R., Gross, M.H.: H-BLOB: a hierarchical visual clustering method using implicit surfaces. In: Visualization 2000. Proceedings, pp. 61–68, October 2000
Van Ham, F., Van Wijk, J.J.: Interactive visualization of small world graphs. In: IEEE Symposium on Information Visualization, pp. 199–206 (2004)
Watanabe, N., Washida, M., Igarashi, T.: Bubble clusters: an interface for manipulating spatial aggregation of graphical objects. In: Proceedings of the 20th Annual ACM Symposium on User Interface Software and Technology, UIST 2007, pp. 173–182. ACM, New York (2007)
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Vihrovs, J., Prūsis, K., Freivalds, K., Ručevskis, P., Krebs, V. (2015). A Potential Field Function for Overlapping Point Set and Graph Cluster Visualization. In: Battiato, S., Coquillart, S., Pettré, J., Laramee, R., Kerren, A., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics - Theory and Applications. VISIGRAPP 2014. Communications in Computer and Information Science, vol 550. Springer, Cham. https://doi.org/10.1007/978-3-319-25117-2_9
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