Graph Drawing by Classical Multidimensional Scaling: New Perspectives

  • Mirza Klimenta
  • Ulrik Brandes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


With shortest-path distances as input, classical multidimensional scaling can be regarded as a spectral graph drawing algorithm, and recent approximation techniques make it scale to very large graphs. In comparison with other methods, however, it is considered inflexible and prone to degenerate layouts for some classes of graphs.

We want to challenge this belief by demonstrating that the method can be flexibly adapted to provide focus+context layouts. Moreover, we propose an alternative instantiation that appears to be more suitable for graph drawing and prevents certain degeneracies.


Multidimensional Scaling Large Graph Graph Drawing Orthonormal Eigenvector Intrinsic Dimensionality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bavaud, F.: On the Schoenberg transformations in data analysis: Theory and illustrations. Journal of Classification 28(3), 297–314 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling: Theory and Applications. Springer (2005)Google Scholar
  3. 3.
    Brandes, U., Pich, C.: Eigensolver Methods for Progressive Multidimensional Scaling of Large Data. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 42–53. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Brandes, U., Pich, C.: An Experimental Study on Distance-Based Graph Drawing. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 218–229. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Buja, A., Swayne, D.F., Littmann, M.L., Dean, N., Hofmann, H.: Xgvis: Interactive data visualization with mds. Journal of Computational and Graphical Statistics (2001)Google Scholar
  6. 6.
    Card, S.K., Mackinlay, J.D., Shneiderman, B. (eds.): Readings in Info. Vis.: Using Vision to Think. Morgan Kaufman Publishers (1999)Google Scholar
  7. 7.
    Civril, A., Magdon-Ismail, M., Bocek-Rivele, E.: SDE: Graph Drawing Using Spectral Distance Embedding. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 512–513. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Çivril, A., Magdon-Ismail, M., Bocek-Rivele, E.: SSDE: Fast Graph Drawing Using Sampled Spectral Distance Embedding. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 30–41. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Cox, T., Cox, M.: Multidimensional Scaling. CRC/Chapman and Hall (2001)Google Scholar
  10. 10.
    France, S.L., Carroll, J.D.: Two-way multidimensional scaling: A review. IEEE Trans. Sys., Man, and Cyber., Part C: Apps. and Reviews 41(5), 644–661 (2011)CrossRefGoogle Scholar
  11. 11.
    Furnas, G.W.: Generalized fisheye views. In: Proc. ACM SIGCHI Conf. Human Factors in Comp. Sys., pp. 16–23. ACM Press (1986)Google Scholar
  12. 12.
    Gajer, P., Goodrich, M.T., Kobourov, S.G.: A Multi-dimensional Approach to Force-Directed Layouts of Large Graphs. In: Marks, J. (ed.) GD 2000. LNCS, vol. 1984, pp. 211–221. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Gansner, E., Koren, Y., North, S.: Topological fisheye views for visualizing large graphs. IEEE Trans. Vis. and Comp. Graph. 11(4), 457–468 (2005)CrossRefGoogle Scholar
  14. 14.
    Gansner, E.R., Koren, Y., North, S.: Graph Drawing by Stress Majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Gower, J.C.: Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53, 325–338 (1966)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Gower, J.C.: Euclidean distance geometry. Math. Scientist. 7, 1–14 (1982)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Gower, J.C.: Properties of Euclidean and non-Euclidean distance matrices. Linear Algebra and Its Applications 67, 81–97 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Hall, K.M.: An r-dimensional quadratic placement algorithm. Management Science 17, 219–229 (1970)zbMATHCrossRefGoogle Scholar
  19. 19.
    Harel, D., Koren, Y.: Graph Drawing by High-Dimensional Embedding. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 207–219. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Hosobe, H.: A high-dimensional approach to interactive graph visualization. In: Proc. of ACM Symp. on Applied Comp., pp. 1253–1257. ACM (2004)Google Scholar
  21. 21.
    Hosobe, H.: An extended high-dimensional method for interactive graph drawing. In: Proc. of the Asia-Pac. Info. Vis., pp. 15–20. Austral. Comp. Soc. (2005)Google Scholar
  22. 22.
    Kaugars, K., Reinfelds, J., Brazma, A.: A Simple Algorithm for Drawing Large Graphs on Small Screens. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 278–281. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  23. 23.
    Keahey, T.A., Robertson, E.L.: Techniques for non-linear magnification transformations. In: Proc. IEEE Symp. Info. Vis., pp. 38–46. IEEE Comp. Soc. (1996)Google Scholar
  24. 24.
    Koren, Y., Carmel, L.: Visualization of labeled data using linear transformations. In: Proc. IEEE Symp. Info. Vis., pp. 121–128. IEEE Comp. Soc. (2003)Google Scholar
  25. 25.
    Koren, Y., Carmel, L.: Robust linear dimensionality reduction. IEEE Trans. Vis. and Compr. Graph. 10(4), 459–470 (2004)CrossRefGoogle Scholar
  26. 26.
    Kruskal, J.B., Seery, J.B.: Designing network diagrams. In: Proc. of the 1st Gen. Conf. on Soc. Graph., pp. 22–50 (1980)Google Scholar
  27. 27.
    Misue, K., Sugiyama, K.: Multi-viewpoint perspective display methods: Formulation and application to compound graphs. In: Proc. Conf. on HCI, pp. 834–838. Elsevier (1991)Google Scholar
  28. 28.
    Sarkar, M., Brown, M.H.: Graphical fisheye views of graphs. In: Proc. Conf. on HCI, pp. 83–91. ACM (1992)Google Scholar
  29. 29.
    de Silva, V., Tenenbaum, J.B.: Global versus local methods in nonlinear dimensionality reduction. In: Adv. Neur. Info. Process. Sys., vol. 15, pp. 705–712. MIT Press (2003)Google Scholar
  30. 30.
    Storey, M.D., David Fracchia, F., Mueller, H.A.: Customizing a fisheye view algorithm to preserve the mental map. Jour. Vis. Lang. Comp. 10(3), 245–267 (1999)CrossRefGoogle Scholar
  31. 31.
    Torgerson, W.S.: Multidimensional scaling: I. Theory and method. Psychometrika 17(4), 401–419 (1952)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Tzeng, J., Lu, H.H.S., Li, W.H.: Multidimensional scaling for large genomic datasets. BMC Bioinformatics 9(1), 179–197 (2008)CrossRefGoogle Scholar
  33. 33.
    Webb, A.R.: Statistical Pattern Recognition. John Wiley & Sons (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mirza Klimenta
    • 1
  • Ulrik Brandes
    • 1
  1. 1.Department of Computer & Information ScienceUniversity of KonstanzGermany

Personalised recommendations