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Spring-Based Lattice Drawing Highlighting Conceptual Similarity

  • Conference paper
Formal Concept Analysis

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3874))

Abstract

This paper presents a spring-based lattice drawing method that uses natural spring lengths determined by assigning a dissimilarity value, the size of symmetric difference, to every pair of concept extents. This extends previous work on incorporating support structure in a concept lattice diagram, in which the support weight function was applied to modify any layout. That work was a partial advance toward the goal of viewing high confidence association rules via the lattice diagram in a way that naturally extends the traditional viewing of implications in a diagram, but also caused the appearance of nearly horizontal edges. The spring-based method solves this problem by placing concepts in the ambient space such that the distance between concepts is proportional to the size of the symmetric difference of the extents of the respective concepts. Besides meeting the proportionality criteria, the algorithm yields highly symmetric diagrams in cases where it is expected.

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References

  1. Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, NJ (1999)

    MATH  Google Scholar 

  2. Cole, R.J.: Automatic Layout of Concept Lattices using Layer Diagrams and Additive Diagrams. In: Oudshoorn, M. (ed.) Proceedings of the 24th Australasian Conference on Computer science, Gold Coast, Queensland, Australian Computer Science Communications, vol. 23, pp. 47–53. IEEE Computer Society, Los Alamitos (2001)

    Google Scholar 

  3. Freese, R.: LatDrawWin, a lattice drawing applet, available at http://www.math.hawaii.edu/~ralph/LatDraw

  4. Freese, R.: Automated Lattice Drawing. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 112–127. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. University of Montreal, Galicia - Galois Lattice Interactive Constructor, http://www.iro.umontreal.ca/~galicia/visualization.html

  6. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, pp. 68–79. Springer, New York (1999)

    MATH  Google Scholar 

  7. Hettich, S., Bay, S.D.: The UCI KDD Archive. University of California, Department of Information and Computer Science, Irvine (1999), http://kdd.ics.uci.edu

    Google Scholar 

  8. Pogel, A., Hannan, T., Miller, L.: Visualization of Concept Lattices Using Weight Functions. In: Supplementary Proceedings of ICCS 2004, Shaker (2004)

    Google Scholar 

  9. Langsdorf, R., Skorsky, M., Wille, R., Wolf, A.: An Approach to Automated Drawing of Concept Lattices. Technical Report 1874, Technical University of Darmstadt, Schlossgatenstasse, Darmstadt, Germany (1996)

    Google Scholar 

  10. Ozonoff, D., Pogel, A., Hannan, T.: Generalized Contingency Tables and Concept Lattices. In: Abello, J., Cormode, G. (eds.) AMS-DIMACS Special Volume: Discrete Methods in Epidemiology, AMS (2006) (to appear)

    Google Scholar 

  11. For higher resolution images of various Figures in this paper and additional images of the results of the drawing algorithm, go to, http://www.psl.nmsu.edu/apogel/SpringBasedLatticeDrawing

  12. Stumme, G., Taouil, R., Bastide, Y., Pasquier, N., Lakhal, L.: Computing iceberg concept lattices with Titanic. Data and Knowledge Engineering 42, 189–222 (2002)

    Article  MATH  Google Scholar 

  13. Stumme, G., Wille, R.: A Geometrical Heuristic for Drawing Concept Lattices. In: Graph Drawing, pp. 452–460. Springer, Heidelberg (1995)

    Google Scholar 

  14. Yevtushenko, S., et al.: Concept Explorer, Open source java software, Release 1.2 (2003), available at http://sourceforge.net/projects/conexp

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Author information

Authors and Affiliations

  1. Physical Science Laboratory, New Mexico State University, Las Cruces, NM, 88003, USA

    Tim Hannan & Alex Pogel

Authors
  1. Tim Hannan
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  2. Alex Pogel
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Editor information

Editors and Affiliations

  1. Département d’informatique et d’ingénierie, Université du Québec en Outaouais, succursale B, C.P. 1250, J8X 3X7, Gatineau, Québec, Canada

    Rokia Missaoui

  2. Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland

    Jürg Schmidt

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© 2006 Springer-Verlag Berlin Heidelberg

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Hannan, T., Pogel, A. (2006). Spring-Based Lattice Drawing Highlighting Conceptual Similarity. In: Missaoui, R., Schmidt, J. (eds) Formal Concept Analysis. Lecture Notes in Computer Science(), vol 3874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671404_18

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  • DOI: https://doi.org/10.1007/11671404_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32203-0

  • Online ISBN: 978-3-540-32204-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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