Abstract
In this paper we propose a simple way of significantly improving the performance of the Softassign graph-matching algorithm of Gold and Rangarajan. Exploiting recent theoretical results in spectral graph theory we use diffusion kernels to transform a matching problem between unweighted graphs into a matching between weighted ones in which the weights rely on the entropies of the probability distributions associated to the vertices after kernel computation. In our experiments, we report that weighting the original quadratic cost function results in a notable improvement of the matching performance, even in medium and high noise conditions.
Chapter PDF
Similar content being viewed by others
Keywords
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
Chung, F.R.K.: Spectral Graph Theory. Conference Board of the Mathematical Sciences (CBMS), vol. 92. American Mathematical Society, Providence (1997)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)
Gärtner: A Survey of Kernels for Structured Data. ACM SIGKDD Explorations Newsletter 5(1), 49–58 (2003)
Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)
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)
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)
Müller, K.-R., Mika, S., Räshc, Tsuda, K., Schölkopf, B.: An Introduction to Kernel-based Learning Algorithms. IEEE Transactions on Neural Networks 12(2), 181–201 (2001)
Pelillo, M.: Replicator Equations, Maximal Cliques, and Graph Isomorphism. Neural Computation 11, 1933–1955 (1999)
Robles-Kelly, A., Hancock, E.: Graph Matching Using Spectral Seriation. In: Rangarajan, A., Figueiredo, M.A.T., Zerubia, J. (eds.) EMMCVPR 2003. LNCS, vol. 2683, pp. 517–532. Springer, Heidelberg (2003)
Sinkhorn, R.: A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices. Annals of Mathematical Statistics 35, 876–879 (1964)
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)
Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)
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)
DePiero, F.W., Trivedi, M., Serbin, S.: Graph Matching Using a Direct Classification of Node Attendance. Pattern Recognition 29(6), 1031–1048 (1996)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lozano, M.A., Escolano, F. (2004). A Significant Improvement of Softassign with Diffusion Kernels. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2004. Lecture Notes in Computer Science, vol 3138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27868-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-27868-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22570-6
Online ISBN: 978-3-540-27868-9
eBook Packages: Springer Book Archive