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An Eigenspace Projection Clustering Method for Inexact Graph Matching
April 2004 (vol. 26 no. 4)
pp. 515-519

Abstract—In this paper, we show how inexact graph matching (that is, the correspondence between sets of vertices of pairs of graphs) can be solved using the renormalization of projections of the vertices (as defined in this case by their connectivities) into the joint eigenspace of a pair of graphs and a form of relational clustering. An important feature of this eigenspace renormalization projection clustering (EPC) method is its ability to match graphs with different number of vertices. Shock graph-based shape matching is used to illustrate the model and a more objective method for evaluating the approach using random graphs is explored with encouraging results.

[1] D. Davies and D. Bouldin, A Cluster Separation Measure IEEE Trans. Pattern Recognition and Machine Intelligence, vol. 1, no. 2, pp. 224-227, 1979.
[2] J.S. Ide and F.G. Cozman, Generating Random Bayesian Networks Proc. Brazilian Symp. Artificial Intelligence, 2002.
[3] S. Lee, J. Kim, Attributed Strokegraph Matching for Seal Imprint Verification Pattern Recognition Letters, vol. 9, pp. 137-145, 1989.
[4] B. Luo and E.R. Hancock, Structural Matching Using the Em Algorithm and Singular Value Decomposition IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, pp. 1120-1136, 2001.
[5] M. Pelillo, K. Siddiqi, and S.W. Zucker, Many-to-Many Matching of Attributed Trees Using Association Graphs and Game Dynamics Visual Form 2001, Lecture Notes in Computer Science, vol. 2059, pp. 583-593, Springer, 2001.
[6] S. Sclaroff and A.P. Pentland, Modal Matching for Correspondence and Recognition IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 6, pp. 545-561, 1995.
[7] G. Scott and H. Longuet-Higgins, An Algorithm for Associating the Features of Two Patterns Proc. Royal Soc. London, vol. B244, 1991.
[8] L. Shapiro and J. Brady, Feature-Based Correspondence An Eigenvector Approach Proc. Int'l Verilog HDL Conf., vol. 10, 1992.
[9] L. Shapiro and J. Brady, Feature-Based Correspondence An Eigenvector Approach Image and Vision Computing, vol. 10, pp. 268-281, 1992.
[10] K. Siddiqi, S. Bouix, A. Tannebaum, and S. Zucker, Hamilton-Jacobi Skeletons Int'l J. Computer Vision, to appear.
[11] K. Siddiqi, A. Shokoufandeh, S. Dickinson, and S. Zucker, Shock Graphs and Shape Matching Int'l J. Computer Vision, vol. 30, pp. 1-24, 1999.
[12] M. Steinbach, G. Karypis, and V. Kumar, A Comparison of Document Clustering Techniques. 2000.
[13] A. van Wyk, T. Tariq, and B. van Wyk, A RKHS Interpolator-Based Graph Matching Algorithm IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 7, pp. 988-995, July 2002.
[14] S. Wu, Y. Ren, and C. Suen, Hierarchical Attributed Graph Representation and Recognition of Handwritten Chineese Characters Pattern Recognition, vol. 24, pp. 617-632, 1991.
[15] W. Zwick and W. Velicer, Comparison of Five Rules for Determining the Number of Components to Retain Psychological Bull., vol. 99, 1986.

Index Terms:
Inexact multisubgraph matching, eigendecomposition, eigenspace projections, correspondence clustering, shape matching, random graphs.
Citation:
Terry Caelli, Serhiy Kosinov, "An Eigenspace Projection Clustering Method for Inexact Graph Matching," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 4, pp. 515-519, April 2004, doi:10.1109/TPAMI.2004.1265866
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