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Error-Tolerant Geometric Graph Similarity

  • Shri Prakash Dwivedi
  • Ravi Shankar Singh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11004)

Abstract

Graph matching is the task of computing the similarity between two graphs. Error-tolerant graph matching is a type of graph matching, in which a similarity between two graphs is computed based on some tolerance value whereas within exact graph matching a strict one-to-one correspondence is required between two graphs. In this paper, we present an approach to error-tolerant graph similarity using geometric graphs. We define the vertex distance (dissimilarity) and edge distance between two graphs and combine them to compute graph distance.

Keywords

Graph matching Geometric graph Graph distance 

References

  1. 1.
    Armiti, A., Gertz, M.: Geometric graph matching and similarity: a probabilistic approach. In: SSDBM (2014)Google Scholar
  2. 2.
    Bunke, H.: Error-tolerant graph matching: a formal framework and algorithms. In: Amin, A., Dori, D., Pudil, P., Freeman, H. (eds.) SSPR/SPR 1998. LNCS, vol. 1451, pp. 1–14. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0033223CrossRefGoogle Scholar
  3. 3.
    Bunke, H., Allerman, G.: Inexact graph matching for structural pattern recognition. Pattern Recogn. Lett. 1, 245–253 (1983)CrossRefGoogle Scholar
  4. 4.
    Caelli, T., Kosinov, S.: Inexact graph matching using eigen-subspace projection clustering. Int. J. Pattern Recogn. Artif. Intell. 18(3), 329–355 (2004)CrossRefGoogle Scholar
  5. 5.
    Cheong, O., Gudmundsson, J., Kim, H.-S., Schymura, D., Stehn, F.: Measuring the similarity of geometric graphs. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 101–112. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-02011-7_11CrossRefGoogle Scholar
  6. 6.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. Int. J. Pattern Recogn. Artif. Intell. 18(3), 265–298 (2004)CrossRefGoogle Scholar
  7. 7.
    Dwivedi, S.P., Singh, R.S.: Error-tolerant graph matching using homeomorphism. In: International Conference on Advances in Computing, Communication and Informatics (ICACCI), pp. 1762–1766 (2017)Google Scholar
  8. 8.
    Foggia, P., Percannella, G., Vento, M.: Graph matching and learning in pattern recognition in the last 10 years. Int. J. Pattern Recogn. Artif. Intell. 88, 1450001.1–1450001.40 (2014)MathSciNetGoogle Scholar
  9. 9.
    Gartner, T.: Kernels for Structured Data. World Scientific, Singapore (2008)CrossRefGoogle Scholar
  10. 10.
    Hart, P.E., Nilson, N.J., Raphael, B.: A formal basis for heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4, 100–107 (1968)CrossRefGoogle Scholar
  11. 11.
    Haussler, D.: Convolution kernels on discrete structures. Technical report, UCSC-CRL-99-10, University of California, Sant Cruz (1999)Google Scholar
  12. 12.
    Kuramochi, M., Karypis, G.: Discovering frequent geometric subgraphs. Inf. Syst. 32, 1101–1120 (2007)CrossRefGoogle Scholar
  13. 13.
    Lafferty, J., Lebanon, G.: Diffusion kernels on statistical manifolds. J. Mach. Learn. Res. 6, 129–163 (2005)MathSciNetMATHGoogle Scholar
  14. 14.
    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 /SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006).  https://doi.org/10.1007/11815921_17CrossRefGoogle Scholar
  15. 15.
    Neuhaus, M., Bunke, H.: Bridging the Gap Between Graph Edit Distance and Kernel Machines. World Scientific, Singapore (2007)CrossRefGoogle Scholar
  16. 16.
    Pinheiro, M.A., Kybic, J., Fua, P.: Geometric graph matching using Monte Carlo tree search. IEEE Trans. Pattern Anal. Mach. Intell. 39(11), 2171–2185 (2017)CrossRefGoogle Scholar
  17. 17.
    Robles-Kelly, A., Hancock, E.R.: Graph edit distance from spectral seriation. IEEE Trans. Pattern Anal. Mach. Intell. 27, 365–378 (2005)CrossRefGoogle Scholar
  18. 18.
    Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, N., et al. (eds.) SSPR /SPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Berlin (2008).  https://doi.org/10.1007/978-3-540-89689-0_33CrossRefGoogle Scholar
  19. 19.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image Vis. Comput. 27(4), 950–959 (2009)CrossRefGoogle Scholar
  20. 20.
    Riesen, K., Bunke, H.: Improving bipartite graph edit distance approximation using various search strategies. Pattern Recogn. 48(4), 1349–1363 (2015)CrossRefGoogle Scholar
  21. 21.
    Sanfeliu, A., Fu, K.S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Trans. Syst. Man Cybern. 13(3), 353–363 (1983)CrossRefGoogle Scholar
  22. 22.
    Schieber, T.A., Carpi, L., Diaz-Guilera, A., Pardalos, P.M., Masoller, C., Ravetti, M.G.: Quantification of network structural dissimilarities. Nature Commun. 8(13928), 1–10 (2017)Google Scholar
  23. 23.
    Shimada, Y., Hirata, Y., Ikeguchi, T., Aihara, K.: Graph distance for complex networks. Sci. Rep. 6(34944), 1–6 (2016)Google Scholar
  24. 24.
    Shokoufandeh, A., Macrini, D., Dickinson, S., Siddiqi, K., Zucker, S.: Indexing hierarchical structures using graph spectra. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 365–378 (2005)CrossRefGoogle Scholar
  25. 25.
    Sorlin, S., Solnon, C.: Reactive tabu search for measuring graph similarity. In: Brun, L., Vento, M. (eds.) GbRPR 2005. LNCS, vol. 3434, pp. 172–182. Springer, Heidelberg (2005).  https://doi.org/10.1007/978-3-540-31988-7_16CrossRefMATHGoogle Scholar
  26. 26.
    Tsai, W.H., Fu, K.S.: Error-correcting isomorphisms of attributed relational graphs for pattern analysis. IEEE Trans. Syst. Man Cybern. 9, 757–768 (1979)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology (BHU)VaranasiIndia

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