Dissimilarity Based Vector Space Embedding of Graphs Using Prototype Reduction Schemes

  • Kaspar Riesen
  • Horst Bunke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5632)

Abstract

Graphs provide us with a powerful and flexible representation formalism for object classification. The vast majority of classification algorithms, however, rely on vectorial data descriptions and cannot directly be applied to graphs. In the present paper a dissimilarity representation for graphs is used in order to explicitly transform graphs into n-dimensional vectors. This embedding aims at bridging the gap between the high representational power of graphs and the large amount of classification algorithms available for feature vectors. The basic idea is to regard the dissimilarities to n predefined prototype graphs as features. In contrast to previous works, the prototypes and in particular their number are defined by prototype reduction schemes originally developed for nearest neighbor classifiers. These reduction schemes enable us to omit the cumbersome validation of the embedding space dimensionality. With several experimental results we prove the robustness and flexibility of our new method and show the advantages of graph embedding based on prototypes gained by these reduction strategies.

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References

  1. 1.
    Perner, P. (ed.): MLDM 2007. LNCS (LNAI), vol. 4571. Springer, Heidelberg (2007)MATHGoogle Scholar
  2. 2.
    Perner, P. (ed.): ICDM 2006. LNCS (LNAI), vol. 4065. Springer, Heidelberg (2006)Google Scholar
  3. 3.
    Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley-Interscience, Hoboken (2000)MATHGoogle Scholar
  4. 4.
    Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)CrossRefMATHGoogle Scholar
  5. 5.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. Int. Journal of Pattern Recognition and Artificial Intelligence 18(3), 265–298 (2004)CrossRefGoogle Scholar
  6. 6.
    Cook, D., Holder, L. (eds.): Mining Graph Data. Wiley-Interscience, Hoboken (2007)MATHGoogle Scholar
  7. 7.
    Gärtner, T.: Kernels for Structured Data. World Scientific, Singapore (2008)CrossRefMATHGoogle Scholar
  8. 8.
    Neuhaus, M., Bunke, H.: Bridging the Gap Between Graph Edit Distance and Kernel Machines. World Scientific, Singapore (2007)CrossRefMATHGoogle Scholar
  9. 9.
    Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)CrossRefMATHGoogle Scholar
  10. 10.
    Luo, B., Wilson, R., Hancock, E.: Spectral embedding of graphs. Pattern Recognition 36(10), 2213–2223 (2003)CrossRefMATHGoogle Scholar
  11. 11.
    Wilson, R., Hancock, E., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. on Pattern Analysis ans Machine Intelligence 27(7), 1112–1124 (2005)CrossRefGoogle Scholar
  12. 12.
    Robles-Kelly, A., Hancock, E.: A Riemannian approach to graph embedding. Pattern Recognition 40, 1024–1056 (2007)CrossRefMATHGoogle Scholar
  13. 13.
    Pekalska, E., Duin, R.: The Dissimilarity Representation for Pattern Recognition: Foundations and Applications. World Scientific, Singapore (2005)CrossRefMATHGoogle Scholar
  14. 14.
    Spillmann, B., Neuhaus, M., Bunke, H., Pekalska, E., Duin, R.: Transforming strings to vector spaces using prototype selection. In: Yeung, D.Y., Kwok, J., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 287–296. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    Bezdek, J., Kuncheva, L.: Nearest prototype classifier designs: An experimental study. Int. Journal of Intelligent Systems 16(12), 1445–1473 (2001)CrossRefMATHGoogle Scholar
  17. 17.
    Kim, S., Oommen, B.: On using prototype reduction schemes to optimize dissimilarity-based classification. Pattern Recognition 40, 2946–2957 (2006)CrossRefMATHGoogle Scholar
  18. 18.
    Kim, S., Oommen, B.: A brief taxonomy and ranking of creative prototype reduction schemes. Pattern Analysis and Applications 6, 232–244 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Neuhaus, M., Riesen, K., Bunke, H.: Fast suboptimal algorithms for the computation of graph edit distance. In: Yeung, D.Y., Kwok, J., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image and Vision Computing (2008) (accepted for publication)Google Scholar
  21. 21.
    Vapnik, V.: Statistical Learning Theory. John Wiley, Chichester (1998)MATHGoogle Scholar
  22. 22.
    Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)MATHGoogle Scholar
  23. 23.
    Kohavi, R., John, G.: Wrappers for feature subset selection. Artificial Intelligence 97(1-2), 273–324 (1997)CrossRefMATHGoogle Scholar
  24. 24.
    Hart, P.: The condensed nearest neighbor rule. IEEE Trans. on Information Theory 14(3), 515–516 (1968)CrossRefGoogle Scholar
  25. 25.
    Susheela Devi, V., Murty, M.: An incremental prototype set building technique. Pattern Recognition 35(2), 505–513 (2002)CrossRefMATHGoogle Scholar
  26. 26.
    Devijver, P.A., Kittler, J.: On the edited nearest neighbor rule. In: Proc. 5th Int. Conf. on Pattern Recognition, pp. 72–80 (1980)Google Scholar
  27. 27.
    Gates, G.W.: The reduced nearest neighbor rule. IEEE Transactions on Information Theory 18, 431–433 (1972)CrossRefGoogle Scholar
  28. 28.
    Chang, C.L.: Finding prototypes for nearest neighbor classifiers. IEEE Trans. on Computers 23(11), 1179–1184 (1974)CrossRefMATHGoogle Scholar
  29. 29.
    Ritter, G., Woodruff, H., Lowry, S., Isenhour, T.: An algorithm for a selective nearest neighbor decision rule. IEEE Trans. on Information Theory 21(6), 665–669 (1975)CrossRefMATHGoogle Scholar
  30. 30.
    Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008) (accepted for publication)CrossRefGoogle Scholar
  31. 31.
    DTP, D.T.P.: AIDS antiviral screen (2004), http://dtp.nci.nih.gov/docs/aids/aids_data.html
  32. 32.
    Watson, C., Wilson, C.: NIST Special Database 4, Fingerprint Database. National Institute of Standards and Technology (1992)Google Scholar
  33. 33.
    Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific, Singapore (2005)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

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