Abstract

Graph edit distance is one of the most flexible mechanisms for error-tolerant graph matching. Its key advantage is that edit distance is applicable to unconstrained attributed graphs and can be tailored to a wide variety of applications by means of specific edit cost functions. Its computational complexity, however, is exponential in the number of vertices, which means that edit distance is feasible for small graphs only. In this paper, we propose two simple, but effective modifications of a standard edit distance algorithm that allow us to suboptimally compute edit distance in a faster way. In experiments on real data, we demonstrate the resulting speedup and show that classification accuracy is mostly not affected. The suboptimality of our methods mainly results in larger inter-class distances, while intra-class distances remain low, which makes the proposed methods very well applicable to distance-based graph classification.

References

  1. 1.
    Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics (Part B) 13, 353–363 (1983)MATHGoogle Scholar
  2. 2.
    Hopcroft, J., Wong, J.: Linear time algorithm for isomorphism of planar graphs. In: Proc. 6th Annual ACM Symposium on Theory of Computing, pp. 172–184 (1974)Google Scholar
  3. 3.
    Luks, E.: Isomorphism of graphs of bounded valence can be tested in ploynomial time. Journal of Computer and Systems Sciences 25, 42–65 (1982)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Torsello, A., Hidovic-Rowe, D., Pelillo, M.: Polynomial-time metrics for attributed trees. IEEE Transactions on Pattern Analysis and Machine Intelligence 27, 1087–1099 (2005)CrossRefGoogle Scholar
  5. 5.
    Dickinson, P., Bunke, H., Dadej, A., Kraetzl, M.: On graphs with unique node labels. In: Hancock, E.R., Vento, M. (eds.) GbRPR 2003. LNCS, vol. 2726, pp. 13–23. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Cross, A., Wilson, R., Hancock, E.: Inexact graph matching using genetic search. Pattern Recognition 30, 953–970 (1997)CrossRefGoogle Scholar
  7. 7.
    Christmas, W., Kittler, J., Petrou, M.: Structural matching in computer vision using probabilistic relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 17, 749–764 (1995)CrossRefGoogle Scholar
  8. 8.
    Neuhaus, M., Bunke, H.: An error-tolerant approximate matching algorithm for attributed planar graphs and its application to fingerprint classification. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 180–189. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Hlaoui, A., Wang, S.: A node-mapping-based algorithm for graph matching (to appear, 2006)Google Scholar
  10. 10.
    Hart, P., Nilsson, N., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions of Systems, Science, and Cybernetics 4, 100–107 (1968)CrossRefGoogle Scholar
  11. 11.
    Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)MATHCrossRefGoogle Scholar
  12. 12.
    Le Saux, B., Bunke, H.: Feature selection for graph-based image classifiers. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 147–154. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Neuhaus, M., Bunke, H.: A graph matching based approach to fingerprint classification using directional variance. In: Kanade, T., Jain, A., Ratha, N.K. (eds.) AVBPA 2005. LNCS, vol. 3546, pp. 191–200. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michel Neuhaus
    • 1
  • Kaspar Riesen
    • 1
  • Horst Bunke
    • 1
  1. 1.Institute of Computer Science and Applied MathematicsUniversity of BernBernSwitzerland

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