Abstract
In This paper, we present a generative model to measure the graph similarity, assuming that an observed graph is generated from a template by a Markov random field. The potentials of this random process are characterized by two sets of parameters: the attribute expectations specified by the the template graph, and the variances that can be learned by a maximum likelihood estimator from a collection of samples. Once a sample graph is observed, a max-product loopy belief propagation algorithm is applied to approximate the most probable explanation of the template’s vertices, mapped to the sample’s vertices. As demonstrated by the experiments, compared with other algorithms, the proposed approach performed better for near isomorphic graphs in the typical graph alignment and information retrieval applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bunke, H.: Graph Matching: Theoretical Foundations, Algorithms and Applications. In: Proceedings Vision Interface (2000)
Conte, D., Foggia, P., Sansone, C.: Thirty Years of Graph Matching in Pattern Recognition. International Journal of Pattern Recognition and Artificial Intelligence 18, 265–298 (2004)
Ullmann, J.R.: An Algorithm for Subgraph Isomorphism. Journal of ACM 23(1), 31–42 (1976)
Egozi, A., Keller, Y., Guterman, H.: A Probabilistic Approach to Spectral Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence (2012)
Bengoetxea, E., Larranaga, P., Bloch, I., et al.: Inexact Graph Matching by Means of Estimation of Distribution Algorithms. Pattern Recognition 35, 2867–2880 (2002)
Melnik, S., Garcia-Molina, H., Rahm, E.: Similarity flooding: A versatile graph matching algorithm and its application to schema matching. In: Proceedings of 18th International Conference on Data Engineering, pp. 117–128 (2002)
Murphy, K.P., Weiss, Y., Jordan, M.I.: Loopy belief propagation for approximate inference: an empirical study. In: Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence, pp. 485–492 (1999)
Sanghavi, S., Malioutov, D., Willsky, A.: Linear Programming Analysis of Loopy Belief Propagation for Weighted Matching. In: Advances in Neural Information Processing Systems, pp. 1281–1288. MIT Press, Cambridge (2007)
Zaslavskiy, M., Bach, F., Vert, J.P.: A Path Following Algorithm for the Graph Matching Problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(12), 2227–2242 (2009)
Yan, X., Zhu, F., Yu, P., Han, J.: Feature-Based Similarity Search in Graph Structures. ACM Transactions on Database Systems 31, 1418–1453 (2006)
Tiakas, E., Papadopoulos, A., Manolopoulos, Y.: Graph Node Clustering via Transitive Node Similarity. In: Proceedings of 14th Panhellenic Conference on Informatics, pp. 72–77 (2010)
Caelli, T., Caetano, T.S.: Graphical models for graph matching: Approximate models and optimal algorithms. Pattern Recognition Letters 26, 339–346 (2005)
Caetano, T.S., McAuley, J.J., Cheng, L., et al.: Learning Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(6), 1048–1058 (2009)
Cour, T., Srinivasan, P., Shi, J.: Balanced graph matching. In: Proc. NIPS, pp. 313–320 (2006)
Jonker, R., Volgenant, A.: A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38(4), 325–340 (1987)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)
Bayati, M., Shah, D., Sharma, M.: Max-Product for Maximum Weight Matching: Convergence, Correctness, and LP Duality. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1241–1251 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shen, G., Li, W. (2012). A Message Passing Graph Match Algorithm Based on a Generative Graphical Model. In: Huang, R., Ghorbani, A.A., Pasi, G., Yamaguchi, T., Yen, N.Y., Jin, B. (eds) Active Media Technology. AMT 2012. Lecture Notes in Computer Science, vol 7669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35236-2_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-35236-2_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35235-5
Online ISBN: 978-3-642-35236-2
eBook Packages: Computer ScienceComputer Science (R0)