Regularization Kernels and Softassign

  • Miguel Angel Lozano
  • Francisco Escolano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3287)


In this paper we analyze the use of regularization kernels on graphs to weight the quadratic cost function used in the Softassign graph-matching algorithm. In a previous work, we have showed that when using diffusion kernels on graphs such a weighting improves significantly the matching performance yielding a slow decay with increasing noise. Weights, relying on the entropies of the probability distributions associated to the vertices after diffusion kernel computation, transform the original unweighted matching problem into a weighted one. In this regard, as diffusion kernels are a particular case of regularization kernels it is interesting to study the utility of this family of kernels for matching purposes. We have designed an experimental set for discovering the optimal performance for each regularization kernel. Our results suggest that kernel combination could be a key point to address in the future.


Edge Density Kernel Computation Graph Match Diffusion Kernel Quadratic Cost Function 
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.


  1. 1.
    Chung, F.R.K.: Spectral Graph Theory. In: Conference Board of the Mathematical Sciences (CBMS), vol. 92, American Mathematical Society, Providence (1997)Google Scholar
  2. 2.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)Google Scholar
  3. 3.
    Gärtner: A Survey of Kernels for Structured Data. ACM SIGKDD Explorations Newsletter 5(1), 49–58 (2003)CrossRefGoogle Scholar
  4. 4.
    Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)CrossRefGoogle Scholar
  5. 5.
    Finch, A.M., Wilson, R.C., Hancock, E.: An Energy Function and Continuous Edit Process for Graph Matching. Neural Computation 10(7), 1873–1894 (1998)CrossRefGoogle Scholar
  6. 6.
    Kondor, R.I., Lafferty, J.: Diffusion Kernels on Graphs and other Discrete Input Spaces. In: Sammut, C., Hoffmann, A.G. (eds.) Machine Learning, Proceedings of the Nineteenth International Conference (ICML 2002), pp. 315–322. Morgan Kaufmann, San Francisco (2002)Google Scholar
  7. 7.
    Lozano, M.A., Escolano, F.: A Significant Improvement of Softassing with Diffusion Kernels. In: Proceedings of the IAPR International Workshop on Syntactical and Structural Pattern Recognition SSPR 2004. LNCS (2004) (accepted for publication)Google Scholar
  8. 8.
    Müller, K.-R., Mika, S., Räshc, T.K., Schölkopf, B.: An Introduction to Kernel-based Learning Algorithms. IEEE Transactions on Neural Networks 12(2), 181–201 (2001)CrossRefGoogle Scholar
  9. 9.
    Schmidt, D.C., Druffel, L.E.: A Fast Backtracking Algorithm to Test Direct Graphs for Isomorphism Using Distance Matrices. Journal of the ACM 23(3), 433–445 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)Google Scholar
  11. 11.
    Smola, A., Schölkopf, B., Müller, K.-R.: The Connection between Regularization Operators and Support Vector Kernels. Neural Networks 11, 637–649 (1998)CrossRefGoogle Scholar
  12. 12.
    Smola, A., Kondor, R.I.: Kernels and Regularization on Graphs. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 144–158. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    DePiero, F.W., Trivedi, M., Serbin, S.: Graph Matching Using a Direct Classification of Node Attendance. Pattern Recognition, Vol 29(6), 1031–1048 (1996)CrossRefGoogle Scholar
  14. 14.
    Ozer, B., Wolf, W., Akansu, A.N.: A Graph Based Object Description for Information Retrieval in Digital Image and Video Libraries. In: Proceedings of the IEEE Workshop on Content-Based Access of Image and Video Libraries, pp. 79–83 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Miguel Angel Lozano
    • 1
  • Francisco Escolano
    • 1
  1. 1.Robot Vision Group, Departamento de Ciencia de la Computación e Inteligencia ArtificialUniversidad de AlicanteSpain

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