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A Comparison between Two Representatives of a Set of Graphs: Median vs. Barycenter Graph

  • Itziar Bardaji
  • Miquel Ferrer
  • Alberto Sanfeliu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6218)

Abstract

In this paper we consider two existing methods to generate a representative of a given set of graphs, that satisfy the following two conditions. On the one hand, that they are applicable to graphs with any kind of labels in nodes and edges and on the other hand, that they can handle relatively large amount of data. Namely, the approximated algorithms to compute the Median Graph via graph embedding and a new method to compute the Barycenter Graph. Our contribution is to give a new algorithm for the barycenter computation and to compare it to the median Graph. To compare these two representatives, we take into account algorithmic considerations and experimental results on the quality of the representative and its robustness, on several datasets.

Keywords

Random Graph 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.

References

  1. 1.
    Wong, A., You, M.: Entropy and distance of random graphs with application to structural pattern recognition. IEEE TPAMI 7, 599–609 (1985)zbMATHGoogle Scholar
  2. 2.
    Serratosa, F., Alquézar, R., Sanfeliu, A.: Synthesis of function-described graphs and clustering of attributed graphs. IJPRAI 16(6), 621–656 (2002)Google Scholar
  3. 3.
    Serratosa, F., Alquézar, R., Sanfeliu, A.: Function-described graphs for modelling objects represented by sets of attributed graphs. Pattern Recognition 36(3), 781–798 (2003)CrossRefGoogle Scholar
  4. 4.
    Serratosa, F., Alquézar, R., Sanfeliu, A.: Estimating the joint probability distribution of random vertices and arcs by means of second-order random graphs. In: Caelli, T.M., Amin, A., Duin, R.P.W., Kamel, M.S., de Ridder, D. (eds.) SPR 2002 and SSPR 2002. LNCS, vol. 2396, pp. 252–262. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Cordella, L.P., Foggia, P., Sansone, C., Vento, M.: Learning structural shape descriptions from examples. Pattern Recognition Letters 23(12), 1427–1437 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Jain, B., Obermayer, K.: On the sample mean of graphs. In: Proc. of IJCNN 2008, June 2008, pp. 993–1000 (2008)Google Scholar
  8. 8.
    Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE TSMC 13(3), 353–362 (1983)zbMATHGoogle Scholar
  9. 9.
    Bunke, H., Günter, S.: Weighted mean of a pair of graphs. Computing 67(3), 209–224 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Münger, A.: Synthesis of prototype graphs from sample graphs. In: Diploma Thesis, University of Bern, in German (1998)Google Scholar
  11. 11.
    Hlaoui, A., Wang, S.: Median graph computation for graph clustering. Soft Comput. 10(1), 47–53 (2006)CrossRefGoogle Scholar
  12. 12.
    Riesen, K., Neuhaus, M., Bunke, H.: Graph embedding in vector spaces by means of prototype selection. In: Escolano, F., Vento, M. (eds.) GbRPR. LNCS, vol. 4538, pp. 383–393. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Bajaj, C.: The algebraic degree of geometric optimization problems. Discrete Comput. Geom. 3(2), 177–191 (1988)zbMATHCrossRefMathSciNetGoogle 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.
    Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: Generalized median graph computation by means of graph embedding in vector spaces. Pattern Recognition 43(4), 1642–1655 (2010)zbMATHCrossRefGoogle Scholar
  16. 16.
    Ferrer, M., Karatzas, D., Valveny, E., Bunke, H.: A recursive embedding approach to median graph computation. In: Torsello, A., Escolano, F., Brun, L. (eds.) GbRPR 2009. LNCS, vol. 5534, pp. 113–123. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    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
  19. 19.
    Riesen, K., Neuhaus, M., Bunke, H.: Bipartite graph matching for computing the edit distance of graphs. In: Escolano, F., Vento, M. (eds.) GbRPR. LNCS, vol. 4538, pp. 1–12. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Bardaji, I.: Graph representatives: Two different approaches based on the median and the barycenter graph. Master’s thesis, UPC, Barcelona (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Itziar Bardaji
    • 1
  • Miquel Ferrer
    • 1
  • Alberto Sanfeliu
    • 1
  1. 1.Institut de Robòtica i Informàtica Industrial, UPC-CSICSpain

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