Abstract
In this paper we propose the use of a simple kernel function based on the graph edit distance. The kernel function allows us to apply a wide range of statistical algorithms to the problem of attributed graph matching. The function we describe is simple to compute and leads to several convenient interpretations of geometric properties of graphs in their implicit vector space representation. Although the function is not generally positive definite, we show in experiments on real-world data that the kernel approach may result in a significant improvement of the graph matching and classification performance using support vector machines and kernel principal component analysis.
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References
Vapnik, V.: Statistical Learning Theory. John Wiley, Chichester (1998)
Byun, H., Lee, S.: A survey on pattern recognition applications of support vector machines. Int. Journal of Pattern Recognition and Art. Intelligence 17, 459–486 (2003)
Müller, K., Mika, S., Rätsch, G., Tsuda, K., Schölkopf, B.: An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks 12, 181–202 (2001)
Watkins, C.: Dynamic alignment kernels. In: Smola, A.J., Bartlett, P.L., Schölkopf, B., Schuurmans, D. (eds.) Advances in Large Margin Classifiers, pp. 39–50. MIT Press, Cambridge (2000)
Gärtner, T., Lloyd, J., Flach, P.: Kernels and distances for structured data. Machine Learning 57, 205–232 (2004)
Haussler, D.: Convolutional kernels on discrete structures. Technical Report UCSC-CRL-99-10, University of California, Santa Cruz (1999)
Kondor, R., Lafferty, J.: Diffusion kernels on graphs and other discrete input spaces. In: Proc. 19th Int. Conf. on Machine Learning, pp. 315–322 (2002)
Kashima, H., Tsuda, K., Inokuchi, A.: Marginalized kernels between labeled graphs. In: Proc. 20th Int. Conf. on Machine Learning, pp. 321–328 (2003)
Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19, 255–259 (1998)
Wallis, W., Shoubridge, P., Kraetzl, M., Ray, D.: Graph distances using graph union. Pattern Recognition Letters 22, 701–704 (2001)
Christmas, W., Kittler, J., Petrou, M.: Structural matching in computer vision using probabilistic relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 17, 749–764 (1995)
Wilson, R., Hancock, E.: Structural matching by discrete relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 19, 634–648 (1997)
Luo, B., Hancock, R.: Structural graph matching using the EM algorithm and singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1120–1136 (2001)
Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics 13, 353–363 (1983)
Myers, R., Wilson, R., Hancock, E.: Bayesian graph edit distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 628–635 (2000)
Messmer, B., Bunke, H.: A new algorithm for error-tolerant subgraph isomorphism detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 493–504 (1998)
Duda, R., Hart, P., Stork, D.: Pattern Classification. John Wiley, Chichester (2000)
Mansilla, E., Ho, T.: On classifier domains of competence. In: Proc. 17th Int. Conf. on Pattern Recognition, vol. 1, pp. 136–139 (2004)
Schölkopf, B., Smolar, A.: Learning With Kernels. MIT Press, Cambridge (2002)
Cover, T.: Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Trans. on Electronic Computers 14, 326–334 (1965)
Berg, C., Christensen, J., Ressel, P.: Harmonic Analysis on Semigroups. Springer, Heidelberg (1984)
Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1144–1151 (2001)
Gill, P., Murray, W., Wright, M.: Practical Optimization. Academic Press, London (1981)
Watson, C., Wilson, C.: NIST Special Database 4. Fingerprint Database. National Institute of Standards and Technology (1992)
Lumini, A., Maio, D., Maltoni, D.: Inexact graph matching for fingerprint classification. Machine Graphics and Vision, Special Issue on Graph Transformations in Pattern Generation and CAD 8, 231–248 (1999)
Neuhaus, M., Bunke, H.: An error-tolerant approximate matching algorithm for attributed planar graphs and its application to fingerprint classification. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 180–189. Springer, Heidelberg (2004)
du Buf, H., Bayer, M.: Automatic Diatom Identification. World Scientific, Singapore (2002)
Ambauen, R., Fischer, S., Bunke, H.: Graph edit distance with node splitting and merging and its application to diatom identification. In: Hancock, E.R., Vento, M. (eds.) GbRPR 2003. LNCS, vol. 2726, pp. 95–106. Springer, Heidelberg (2003)
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Neuhaus, M., Bunke, H. (2005). Edit Distance Based Kernel Functions for Attributed 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_34
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DOI: https://doi.org/10.1007/978-3-540-31988-7_34
Publisher Name: Springer, Berlin, Heidelberg
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