An Inverse Distance-based Potential Field Function for Overlapping Point Set Visualization

Jevgenijs Vihrovs, Krišjānis Prūsis, Kārlis Freivalds, Pēteris Ručevskis, Valdis Krebs

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.

References

  1. Balzer, M. and Deussen, O. (2007). Level-of-detail visualization of clustered graph layouts. 2007 6th International AsiaPacific Symposium on Visualization, pages 133-140.
  2. Blinn, J. F. (1982). A generalization of algebraic surface drawing. ACM Trans. Graph., 1(3):235-256.
  3. Byelas, H. and Telea, A. (2009). Towards realism in drawing areas of interest on architecture diagrams. Journal of Visual Languages Computing, 20(2):110-128.
  4. Collins, C., Penn, G., and Carpendale, S. (2009). Bubble sets: Revealing set relations with isocontours over existing visualizations. IEEE Transactions on Visualization and Computer Graphics, 15(6):1009-1016.
  5. Di Battista, G., Eades, P., Tamassia, R., and Tollis, I. G. (1998). Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall PTR.
  6. Dinkla, K., van Kreveld, M. J., Speckmann, B., and Westenberg, M. A. (2012). Kelp diagrams: Point set membership visualization. Computer Graphics Forum, 31(3pt1):875-884.
  7. Douglas, D. H. and Peucker, T. K. (1973). Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica The International Journal for Geographic Information and Geovisualization, 10(2):112-122.
  8. Gansner, E. R., Hu, Y., and Kobourov, S. (2010). GMap: Visualizing graphs and clusters as maps. 2010 IEEE Pacific Visualization Symposium PacificVis, pages 201- 208.
  9. Goh, K.-I., Cusick, M. E., Valle, D., Childs, B., Vidal, M., and Barabsi, A.-L. (2007). The human disease network. Proceedings of the National Academy of Sciences of the United States of America, 104(21):8685- 8690.
  10. Gross, M. H., Sprenger, T. C., and Finger, J. (1997). Visualizing information on a sphere. In In Proceedings of the 1997 Conference on Information Visualization, pages 11-16.
  11. Heer, J. and Boyd, D. (2003). Vizster: visualizing online social networks. IEEE Symposium on Information Visualization 2005 INFOVIS 2005, 5(page5):32-39.
  12. Hobby, J. D. (1986). Smooth, easy to compute interpolating splines. Discrete and Computational Geometry, 1(2):123-140.
  13. Krebs, V. (2007). Managing the 21st century organization. IHRIM Journal, XI(4):2-8.
  14. Matsumoto, Y., Umano, M., and Inuiguchi, M. (2008). Visualization with Voronoi tessellation and moving output units in self-organizing map of the real-number system. Neural Networks, 1:3428-3434.
  15. Riche, N. H. and Dwyer, T. (2010). Untangling Euler diagrams. IEEE Transactions on Visualization and Computer Graphics, 16(6):1090-1099.
  16. Rosenthal, P. and Linsen, L. (2009). Enclosing surfaces for point clusters using 3D discrete Voronoi diagrams. Computer Graphics Forum, 28(3):999-1006.
  17. Santamara, R. and Thern, R. (2008). Overlapping clustered graphs: Co-authorship networks visualization. Lecture Notes in Computer Science, 5166:190-199.
  18. Simonetto, P., Auber, D., and Archambault, D. (2009). Fully automatic visualisation of overlapping sets. Computer Graphics Forum, 28(3):967-974.
  19. Sprenger, T. C., Brunella, R., and Gross, M. H. (2000). HBLOB: a hierarchical visual clustering method using implicit surfaces. In Visualization 2000. Proceedings, pages 61 -68.
  20. Van Ham, F. and Van Wijk, J. J. (2004). Interactive visualization of small world graphs. IEEE Symposium on Information Visualization, pages 199-206.
  21. Watanabe, N., Washida, M., and Igarashi, T. (2007). 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 7807, pages 173-182, New York, NY, USA. ACM.
Download


Paper Citation


in Harvard Style

Vihrovs J., Prūsis K., Freivalds K., Ručevskis P. and Krebs V. (2014). An Inverse Distance-based Potential Field Function for Overlapping Point Set Visualization . In Proceedings of the 5th International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2014) ISBN 978-989-758-005-5, pages 29-38. DOI: 10.5220/0004681100290038


in Bibtex Style

@conference{ivapp14,
author={Jevgenijs Vihrovs and Krišjānis Prūsis and Kārlis Freivalds and Pēteris Ručevskis and Valdis Krebs},
title={An Inverse Distance-based Potential Field Function for Overlapping Point Set Visualization},
booktitle={Proceedings of the 5th International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2014)},
year={2014},
pages={29-38},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004681100290038},
isbn={978-989-758-005-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Information Visualization Theory and Applications - Volume 1: IVAPP, (VISIGRAPP 2014)
TI - An Inverse Distance-based Potential Field Function for Overlapping Point Set Visualization
SN - 978-989-758-005-5
AU - Vihrovs J.
AU - Prūsis K.
AU - Freivalds K.
AU - Ručevskis P.
AU - Krebs V.
PY - 2014
SP - 29
EP - 38
DO - 10.5220/0004681100290038