A Recursive Embedding Approach to Median Graph Computation

  • M. Ferrer
  • D. Karatzas
  • E. Valveny
  • H. Bunke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5534)


The median graph has been shown to be a good choice to infer a representative of a set of graphs. It has been successfully applied to graph-based classification and clustering. Nevertheless, its computation is extremely complex. Several approaches have been presented up to now based on different strategies. In this paper we present a new approximate recursive algorithm for median graph computation based on graph embedding into vector spaces. Preliminary experiments on three databases show that this new approach is able to obtain better medians than the previous existing approaches.


Edit Operation Graph Database Median Graph Graph Domain Graph Embedding 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific Publishing, USA (2005)CrossRefMATHGoogle Scholar
  2. 2.
    Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1144–1151 (2001)CrossRefGoogle Scholar
  3. 3.
    Münger, A.: Synthesis of prototype graphs from sample graphs. Diploma Thesis, University of Bern (1998) (in German)Google Scholar
  4. 4.
    Hlaoui, A., Wang, S.: Median graph computation for graph clustering. Soft Comput. 10(1), 47–53 (2006)CrossRefGoogle Scholar
  5. 5.
    Ferrer, M., Serratosa, F., Sanfeliu, A.: Synthesis of median spectral graph. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 139–146. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Riesen, K., Neuhaus, M., Bunke, H.: Graph embedding in vector spaces by means of prototype selection. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 383–393. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Bunke, H., Allerman, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1(4), 245–253 (1983)CrossRefMATHGoogle Scholar
  8. 8.
    Bunke, H., Günter, S.: Weighted mean of a pair of graphs. Computing 67(3), 209–224 (2001)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: An approximate algorithm for median graph computation using graph embedding. In: Proceedings of 19th ICPR, pp. 287–297 (2008)Google Scholar
  10. 10.
    Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man and Cybernetics 13(3), 353–362 (1983)CrossRefMATHGoogle Scholar
  11. 11.
    Neuhaus, M., Riesen, K., Bunke, H.: Fast suboptimal algorithms for the computation of graph edit distance. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Riesen, K., Neuhaus, M., Bunke, H.: Bipartite graph matching for computing the edit distance of graphs. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 1–12. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    White, D., Wilson, R.C.: Mixing spectral representations of graphs. In: 18th International Conference on Pattern Recognition (ICPR 2006), Hong Kong, China, August 20-24, pp. 140–144. IEEE Computer Society, Los Alamitos (2006)CrossRefGoogle Scholar
  14. 14.
    Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. Journal (43), 355–386 (1937)Google Scholar
  15. 15.
    Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: SSPR/SPR, pp. 287–297 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Ferrer
    • 1
  • D. Karatzas
    • 2
  • E. Valveny
    • 2
  • H. Bunke
    • 3
  1. 1.Institut de Robòtica i Informàtica Industrial, UPC-CSICBarcelonaSpain
  2. 2.Centre de Visió per Computador, Universitat Autònoma de BarcelonaBellaterraSpain
  3. 3.Institute of Computer Science and Applied MathematicsUniversity of BernBernSwitzerland

Personalised recommendations