A Potential Field Function for Overlapping Point Set and Graph Cluster Visualization

  • Jevgēnijs Vihrovs
  • Krišjānis Prūsis
  • Kārlis Freivalds
  • Pēteris Ručevskis
  • Valdis Krebs
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 550)

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.

Keywords

Information visualization Implicit surfaces 

References

  1. 1.
    Balzer, M., Deussen, O.: Level-of-detail visualization of clustered graph layouts. In: 2007 6th International AsiaPacific Symposium on Visualization, pp. 133–140 (2007)Google Scholar
  2. 2.
    Blinn, J.F.: A generalization of algebraic surface drawing. ACM Trans. Graph. 1(3), 235–256 (1982)CrossRefGoogle Scholar
  3. 3.
    Byelas, H., Telea, A.: Towards realism in drawing areas of interest on architecture diagrams. J. Vis. Lang. Comput. 20(2), 110–128 (2009)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)MATHGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    Heer, J., Boyd, D.: Vizster: visualizing online social networks. In: IEEE Symposium on Information Visualization 2005 INFOVIS 2005, vol. 5, pp. 32–39 (2003)Google Scholar
  12. 12.
    Hobby, J.D.: Smooth, easy to compute interpolating splines. Discrete Comput. Geom. 1(2), 123–140 (1986)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Krebs, V.: Managing the 21st century organization. IHRIM J. XI(4), 2–8 (2007)Google Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    Riche, N.H., Dwyer, T.: Untangling Euler diagrams. IEEE Trans. Vis. Comput. Graph. 16(6), 1090–1099 (2010)CrossRefGoogle Scholar
  16. 16.
    Rosenthal, P., Linsen, L.: Enclosing surfaces for point clusters using 3D discrete Voronoi diagrams. Comput. Graph. Forum 28(3), 999–1006 (2009)CrossRefGoogle Scholar
  17. 17.
    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) CrossRefGoogle Scholar
  18. 18.
    Simonetto, P., Auber, D., Archambault, D.: Fully automatic visualisation of overlapping sets. Comput. Graph. Forum 28(3), 967–974 (2009)CrossRefGoogle Scholar
  19. 19.
    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 2000Google Scholar
  20. 20.
    Van Ham, F., Van Wijk, J.J.: Interactive visualization of small world graphs. In: IEEE Symposium on Information Visualization, pp. 199–206 (2004)Google Scholar
  21. 21.
    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)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Jevgēnijs Vihrovs
    • 1
  • Krišjānis Prūsis
    • 1
  • Kārlis Freivalds
    • 1
  • Pēteris Ručevskis
    • 1
  • Valdis Krebs
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

Personalised recommendations