Abstract

This contribution extends learning vector quantization to the domain of graphs. For this, we first identify graphs with points in some orbifold, then derive a generalized differentiable intrinsic metric, and finally extend the update rule of LVQ for generalized differentiable distance metrics. First experiments indicate that the proposed approach can perform comparable to state-of-the-art methods in structural pattern recognition.

Keywords

Class Label Vector Representation Graph Match Graph Distance Optimal Alignment 
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.
    Almohamad, H., Duffuaa, S.: A linear programming approach for the weighted graph matching problem. IEEE Transactions on PAMI 15(5), 522–525 (1993)Google Scholar
  2. 2.
    Caetano, T.S., Cheng, L., Le, Q.V., Smola, A.J.: Learning graph matching. In: ICCV (2007)Google Scholar
  3. 3.
    Cour, T., Srinivasan, P., Shi, J.: Balanced graph matching. In: NIPS (2006)Google Scholar
  4. 4.
    Dosch, P., Valveny, E.: Report on the second symbol recognition contest. In: Liu, W., Lladós, J. (eds.) GREC 2005. LNCS, vol. 3926, pp. 381–397. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Gold, S., Rangarajan, A.: Graduated Assignment Algorithm for Graph Matching. IEEE Transactions on PAMI 18, 377–388 (1996)Google Scholar
  6. 6.
    Gold, S., Rangarajan, A., Mjolsness, E.: Learning with preknowledge: clustering with point and graph matching distance measures. Neural Computation 8(4), 787–804 (1996)CrossRefGoogle Scholar
  7. 7.
    Günter, S., Bunke, H.: Self-organizing map for clustering in the graph domain. Pattern Recognition Letters 23(4), 405–417 (2002)MATHCrossRefGoogle Scholar
  8. 8.
    Hammer, B., Strickert, M., Villmann, T.: Supervised neural gas with general similarity measure. Neural Processing Letters 21(1), 21–44 (2005)CrossRefGoogle Scholar
  9. 9.
    Jain, B., Wysotzki, F.: Central Clustering of Attributed Graphs. Machine Learning 56, 169–207 (2004)MATHCrossRefGoogle Scholar
  10. 10.
    Jain, B., Obermayer, K.: Structure Spaces. Journal of Machine Learning Research 10, 2667–2714 (2009)MathSciNetGoogle Scholar
  11. 11.
    Kohonen, T.: Self-organizing maps. Springer, Heidelberg (1997)MATHGoogle Scholar
  12. 12.
    Kohonen, T., Somervuo, P.: Self-organizing maps of symbol strings. Neurocomputing 21(1-3), 19–30 (1998)MATHCrossRefGoogle 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)Google Scholar
  14. 14.
    Norkin, V.I.: Stochastic generalized-differentiable functions in the problem of nonconvex nonsmooth stochastic optimization. Cybernetics 22(6), 804–809 (1986)MATHCrossRefGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Riesen, K., Bunke, H.: Graph Classification by Means of Lipschitz Embedding. IEEE Transactions on Systems, Man, and Cybernetics 39(6), 1472–1483 (2009)CrossRefGoogle Scholar
  17. 17.
    Sidere, N., Heroux, P., Ramel, J.-Y.: Vector Representation of Graphs: Application to the Classification of Symbols and Letters. In: Conference Proceedings on Document Analysis and Recognition, pp. 681–685 (2009)Google Scholar
  18. 18.
    Sumervuo, P., Kohonen, T.: Self-organizing maps and learning vector quantization for feature sequences. Neural Processing Letters 10(2), 151–159 (1999)CrossRefGoogle Scholar
  19. 19.
    Umeyama, S.: An eigendecomposition approach to weighted graph matching problems. IEEE Transactions on PAMI 10(5), 695–703 (1988)MATHGoogle Scholar
  20. 20.
    Watson, C., Wilson, C.: NIST Special Database 4, Fingerprint Database. National Institute of Standards and Technology (1992)Google Scholar
  21. 21.
    Van Wyk, M., Durrani, M., Van Wyk, B.: A RKHS interpolator-based graph matching algorithm. IEEE Transactions on PAMI 24(7), 988–995 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Brijnesh J. Jain
    • 1
  • S. Deepak Srinivasan
    • 1
  • Alexander Tissen
    • 1
  • Klaus Obermayer
    • 1
  1. 1.Berlin Institute of TechnologyGermany

Personalised recommendations