Advertisement

Approximate Graph Edit Distance Guided by Bipartite Matching of Bags of Walks

  • Benoit Gaüzère
  • Sébastien Bougleux
  • Kaspar Riesen
  • Luc Brun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8621)

Abstract

The definition of efficient similarity or dissimilarity measures between graphs is a key problem in structural pattern recognition. This problem is nicely addressed by the graph edit distance, which constitutes one of the most flexible graph dissimilarity measure in this field. Unfortunately, the computation of an exact graph edit distance is known to be exponential in the number of nodes. In the early beginning of this decade, an efficient heuristic based on a bipartite assignment algorithm has been proposed to find efficiently a suboptimal solution. This heuristic based on an optimal matching of nodes’ neighborhood provides a good approximation of the exact edit distance for graphs with a large number of different labels and a high density. Unfortunately, this heuristic works poorly on unlabeled graphs or graphs with a poor diversity of neighborhoods. In this work we propose to extend this heuristic by considering a mapping of bags of walks centered on each node of both graphs.

Keywords

Edit Distance Label Graph Quadratic Assignment Problem Cost Matrix Edge Label 
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.
    Bunke, H.: On a relation between graph edit distance and maximum common subgraph. Pattern Recognition Letters 18(9), 689–694 (1997)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)zbMATHCrossRefGoogle Scholar
  3. 3.
    Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. SIAM (2009)Google Scholar
  4. 4.
    Hammack, R., Imrich, W., Klavžar, S.: Hanbook of Product Graphs, 2nd edn. Discrete Mathematics and its Applications. CRC Press, Taylor & Francis (2011)Google Scholar
  5. 5.
    Kuhn, H.W.: The hungarian method for the assignment problem. Naval Research Logistics Quaterly 2, 83–97 (1955)CrossRefGoogle Scholar
  6. 6.
    Munkres, J.: Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics 5(1), 32–38 (1957)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image and Vision Computing 27, 950–959 (2009)CrossRefGoogle Scholar
  8. 8.
    Riesen, K., Emmenegger, S., Bunke, H.: A novel software toolkit for graph edit distance computation. In: Kropatsch, W.G., Artner, N.M., Haxhimusa, Y., Jiang, X. (eds.) GbRPR 2013. LNCS, vol. 7877, pp. 142–151. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. Systems, Man and Cybernetics 13(3), 353–363 (1983)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Benoit Gaüzère
    • 1
  • Sébastien Bougleux
    • 2
  • Kaspar Riesen
    • 3
  • Luc Brun
    • 1
  1. 1.ENSICAEN, GREYC CNRS UMR 6072France
  2. 2.Université de Caen Basse-Normandie, GREYC CNRS UMR 6072France
  3. 3.University of Applied Sciences and Arts Northwestern SwitzerlandSwitzerland

Personalised recommendations