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Local Entropic Graphs for Globally-Consistent Graph Matching

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Graph-Based Representations in Pattern Recognition (GbRPR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3434))

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Abstract

In this paper we propose a novel approach to obtain unambiguous and robust node attributes for matching non-attributed graphs. Such approach consists of exploiting the information coming from diffusion kernels to embed the subgraph induced by the neighborhood of each vertex in an Euclidean manifold and then use entropic graphs for measuring the α–entropy of the resulting distribution. Our experiments with random-generated graphs with 50 nodes show that at low edge densities, where the effect of structural noise is higher, this approach outperforms the description of the subgraph only in terms of diffusion kernels. Furthermore, our structural recognition experiments show that the approach has a practical application. All experiments were performed by weighting the well-known quadratic cost function used in the Softassign algorithm.

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References

  1. Bai, X., Hancock, E.: Heat kernels, manifolds and graph embedding. In: Fred, A. (ed.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 198–206. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Bearwood, J., Halton, J.H., Hammersley, J.M.: The Shortest Path Through Many Points. Proc. Cambridge Philosophical Society 55, 299–327 (1959)

    Article  Google Scholar 

  3. Belkin, M., Niyogi, P.: Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. Neural Information Processing Systems 14, 634–640 (2002)

    Google Scholar 

  4. Bunke, H.: Recent Developments in Graph Matching. In: Proceedings of the International Conference on Pattern Recognition (ICPR 2000), vol. 2, pp. 2117–2124 (2000)

    Google Scholar 

  5. Bunke, H.: Error Correcting Graph Matching: On the Influence of the Underlying Cost Function. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(9), 917–922 (1999)

    Article  Google Scholar 

  6. Costa, J., Hero, A.O.: Geodesic Entropic Graphs for Dimension and Entropy Estimation in Manifold Learning. IEEE Transactions on Signal Processing 52(8), 2210–2221 (2004)

    Article  MathSciNet  Google Scholar 

  7. Chung, F.R.K.: Spectral Graph Theory. In: Conference Board of the Mathematical Sciences (CBMS), vol. 92. American Mathematical Society, Providence (1997)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)

    Article  Google Scholar 

  10. Hero, A.O., Ma, B., Michel, O., Gorman, J.D.: Applications of Entropic Spanning Graphs. IEEE Signal Processing Magazine 19(5), 85 (2002)

    Article  Google Scholar 

  11. Jiang, X., Münger, A., Bunke, H.: On Median Graphs: Properties, Algorithms, and Applications. IEEE Trans. on Pattern Analysis and Machine Intelligence 23(10), 1144–1151 (2001)

    Article  Google Scholar 

  12. Kondor, R.I., Lafferty, J.: Diffusion Kernels on Graphs and other Discrete Input Spaces. In: Sammut, C., et al. (eds.) ICML 2002, pp. 315–322. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  13. Lafferty, J., Lebanon, G.: Diffusion Kernels on Statistical Manifolds. CMU Technical Report CMU-04-101 (2004)

    Google Scholar 

  14. Lozano, M.A., Escolano, F.: EM Algorithm for Clustering an Ensemble of Graphs with Comb Matching. In: Rangarajan, A., Figueiredo, M.A.T., Zerubia, J. (eds.) EMMCVPR 2003. LNCS, vol. 2683, pp. 52–67. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Lozano, M.A., Escolano, F.: A significant improvement of softassign with diffusion kernels. In: Fred, A., et al. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 76–84. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  16. Lozano, M.A., Escolano, F.: Regularization kernels and softassign. In: Sanfeliu, A., et al. (eds.) CIARP 2004. LNCS, vol. 3287, pp. 321–328. Springer, Heidelberg (2004)

    Google Scholar 

  17. Lozano, M.A., Escolano, F.: Structural recognition with kernelized softassign. In: Lemaître, C., et al. (eds.) IBERAMIA 2004. LNCS, vol. 3315, pp. 626–635. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Luo, B., Hancock, E.R.: Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition. IEEE Trans. on Pattern Analysis and Machine Intelligence 23(10), 1120–1136 (2001)

    Article  Google Scholar 

  19. Luo, B., Wilson, R.C., Hancock, E.R.: A spectral approach to learning structural variations in graphs. In: Crowley, J.L., et al. (eds.) ICVS 2003. LNCS, vol. 2626, pp. 407–417. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  20. Pelillo, M.: Replicator Equations, Maximal Cliques, and Graph Isomorphism. Neural Computation 11, 1933–1955 (1999)

    Article  Google Scholar 

  21. Rényi, A.: On Measures of Entropy and Information. In: Proc. 4th Berkeley Symp. Math. Stat. and Prob., vol. 1, pp. 547–561 (1961)

    Google Scholar 

  22. Robles-Kelly, A., Hancock, E.R.: Graph Matching Using Spectral Seriation. In: Rangarajan, A., et al. (eds.) EMMCVPR 2003. LNCS, vol. 2683, pp. 517–532. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  23. Sanfeliu, A., Fu, K.S.: A Distance Measure Between Attributed Relational Graphs for Pattern Recognition. IEEE Transactions on Systems, Man, and Cybernetics 13, 353–362 (1983)

    MATH  Google Scholar 

  24. Serratosa, F., Alquézar, R., Sanfeliu, A.: Function-described graphs for modelling objects represented by sets of attributed graphs. Pattern Recognition 23(3), 781–798 (2003)

    Article  Google Scholar 

  25. Smola, A., Kondor, R.I.: Kernels and regularization on graphs. In: Schölkopf, et al. (eds.) COLT/Kernel 2003. LNCS, vol. 2777, pp. 144–158. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  26. Wilson, R.C., Hancock, E.R.: Structual Matching by Discrete Relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(6), 634–648 (1997)

    Article  Google Scholar 

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Lozano, M.A., Escolano, F. (2005). Local Entropic Graphs for Globally-Consistent Graph Matching. In: Brun, L., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2005. Lecture Notes in Computer Science, vol 3434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31988-7_33

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  • DOI: https://doi.org/10.1007/978-3-540-31988-7_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25270-2

  • Online ISBN: 978-3-540-31988-7

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