This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Learning Graph Matching
June 2009 (vol. 31 no. 6)
pp. 1048-1058
ASCII Text
x 
 
Tibério S. Caetano, Julian J. McAuley, Li Cheng, Quoc V. Le, Alex J. Smola, "Learning Graph Matching," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 6, pp. 1048-1058, June, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2009.28,
author = {Tibério S. Caetano and Julian J. McAuley and Li Cheng and Quoc V. Le and Alex J. Smola},
title = {Learning Graph Matching},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {31},
number = {6},
issn = {0162-8828},
year = {2009},
pages = {1048-1058},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2009.28},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - Learning Graph Matching
IS - 6
SN - 0162-8828
SP1048
EP1058
EPD - 1048-1058
A1 - Tibério S. Caetano,
A1 - Julian J. McAuley,
A1 - Li Cheng,
A1 - Quoc V. Le,
A1 - Alex J. Smola,
PY - 2009
KW - Graph matching
KW - Learning
KW - Support Vector Machines
KW - Structured Estimation
KW - Optimization
VL - 31
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
Tibério S. Caetano, NICTA and Australian National University, Australia
Julian J. McAuley, NICTA and Australian National University, Australia
Li Cheng, TTI-Chicago, Chicago
Quoc V. Le, Stanford University, Stanford
Alex J. Smola, Yahioo! Research, Santa Clara
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

[1] T.S. Caetano, L. Cheng, Q.V. Le, and A.J. Smola, “Learning Graph Matching,” Proc. Int'l Conf. Computer Vision, 2007.
[2] B. Schölkopf and A. Smola, Learning with Kernels. MIT Press, 2002.
[3] J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis. Cambridge Univ. Press, 2004.
[4] S. Vishwanathan, K.M. Borgwardt, N. Schraudolph, and I.R. Kondor, “On Graph Kernels,” J. Machine Learning Research, submitted, 2008.
[5] A. Torsello and E.R. Hancock, “Learning Shape-Classes Using a Mixture of Tree-Unions,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 6, pp.954-967, June 2006.
[6] D. White and R.C. Wilson, “Spectral Generative Models for Graphs,” Proc. Int'l Conf. Image Analysis and Processing, pp.35-42, 2007.
[7] B. Bonev, F. Escolano, M. Lozano, P. Suau, M. Cazorla, and W. Aguilar, “Constellations and the Unsupervised Learning of Graphs,” Proc. Graph-Based Representations in Pattern Recognition, pp.340-350, 2007.
[8] M. Neuhaus and H. Bunke, “Automatic Learning of Cost Functions for Graph Edit Distance,” Information Sciences, vol. 177, no. 1, pp.239-247, 2007.
[9] M. Leordeanu and M. Hebert, “A Spectral Technique for Correspondence Problems Using Pairwise Constraints,” Proc. Int'l Conf. Computer Vision, 2005.
[10] H. Wang and E.R. Hancock, “A Kernel View of Spectral Point Pattern Matching,” Proc. Int'l Workshops Advances in Structural and Syntactic Pattern Recognition and Statistical Techniques in Pattern Recognition, pp.361-369, 2004.
[11] L. Shapiro and J. Brady, “Feature-Based Correspondence—An Eigenvector Approach,” Image and Vision Computing, vol. 10, pp.283-288, 1992.
[12] M. Carcassoni and E.R. Hancock, “Spectral Correspondence for Point Pattern Matching,” Pattern Recognition, vol. 36, pp.193-204, 2003.
[13] T. Caelli and S. Kosinov, “An Eigenspace Projection Clustering Method for Inexact Graph Matching,” IEEE Trans. Pattern Analayis and Machine Intelligence, vol. 26, no. 4, pp.515-519, Apr. 2004.
[14] T.S. Caetano, T. Caelli, and D.A.C. Barone, “Graphical Models for Graph Matching,” Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, pp.466-473, 2004.
[15] A. Rosenfeld and A.C. Kak, Digital Picture Processing. Academic Press, 1982.
[16] R.C. Wilson and E.R. Hancock, “Structural Matching by Discrete Relaxation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 6, pp.634-648, June 1997.
[17] E. Hancock and R.C. Wilson, “Graph-Based Methods for Vision: A Yorkist Manifesto,” Proc. Int'l Workshops Advances in Structural and Syntactic Pattern Recognition and Statistical Techniques in Pattern Recognition, pp.31-46, 2002.
[18] W.J. Christmas, J. Kittler, and M. Petrou, “Structural Matching in Computer Vision Using Probabilistic Relaxation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp.749-764, 1995.
[19] J.V. Kittler and E.R. Hancock, “Combining Evidence in Probabilistic Relaxation,” Int'l J. Pattern Recognition and Artificial Intelligence, vol. 3, pp.29-51, 1989.
[20] S.Z. Li, “A Markov Random Field Model for Object Matching Under Contextual Constraints,” Proc. IEEE Int'l Conf. Computer Vision and Pattern Recognition, pp.866-869, 1994.
[21] C. Schellewald, “Convex Mathematical Programs for Relational Matching of Object Views,” PhD dissertation, Univ. of Mannhein, 2004.
[22] M. Pelillo, “Replicator Equations, Maximal Cliques, and Graph Isomorphism,” Neural Computation, vol. 11, pp.1933-1955, 1999.
[23] B.T. Messmer and H. Bunke, “A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp.493-503, May 1998.
[24] S. Gold and A. Rangarajan, “A Graduated Assignment Algorithm for Graph Matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 4, pp.377-388, Apr. 1996.
[25] M. van Wyk, T. Durrani, 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.
[26] A. Rangarajan, A. Yuille, and E. Mjolsness, “Convergence Properties of the Softassign Quadratic Assignment Algorithm,” Neural Computation, vol. 11, pp.1455-1474, 1999.
[27] R. Sinkhorn, “A Relationship between Arbitrary Positive Matrices and Doubly Stochastic Matrices,” Annals Math. and Statistics, vol. 35, pp.876-879, 1964.
[28] M. Pelillo and M. Refice, “Learning Compatibility Coefficients for Relaxation Labeling Processes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 9, pp.933-945, Sept. 1994.
[29] S. Lacoste-Julien, B. Taskar, D. Klein, and M. Jordan, “Word Alignment Via Quadratic Assignment,” Proc. North Am. Chapter Assoc. for Computational Linguistics-Human Language Technologies, 2006.
[30] T. Cour, P. Srinivasan, and J. Shi, “Balanced Graph Matching,” Proc. Conf. Neural Information Processing Systems, 2006.
[31] K. Anstreicher, “Recent Advances in the Solution of Quadratic Assignment Problems,” Math. Programming, Ser. B, vol. 97, pp.27-42, 2003.
[32] C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. Dover Publications, July 1998.
[33] I. Tsochantaridis, T. Joachims, T. Hofmann, and Y. Altun, “Large Margin Methods for Structured and Interdependent Output Variables,” J. Machine Learning Research, vol. 6, pp.1453-1484, 2005.
[34] R.K. Ahuja and J.B. Orlin, “Inverse Optimization,” Operations Research, vol. 49, no. 5, pp.771-783, 2001.
[35] A. Smola, S.V.N. Vishwanathan, and Q. Le, “Bundle Methods for Machine Learning,” Proc. Advances in Neural Information Processing Systems 20, J. Platt, D. Koller, Y. Singer, and S. Roweis, eds., pp.1377-1384, 2008.
[36] B. Taskar, C. Guestrin, and D. Koller, “Max-Margin Markov Networks” Proc. Advances in Neural Information Processing Systems 16, S.Thrun, L. Saul, and B. Schölkopf, eds., 2004.
[37] T. Joachims, “Training Linear SVMs in Linear Time,” Proc. Knowledge Discovery and Data Mining, 2006.
[38] C. Teo, Q. Le, A. Smola, and S. Vishwanathan, “A Scalable Modular Convex Solver for Regularized Risk Minimization,” Proc. Knowledge Discovery and Data Mining, 2007.
[39] R. Jonker and A. Volgenant, “A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems,” Computing, vol. 38, no. 4, pp.325-340, 1987.
[40] T. Finley and T. Joachims, “Training Structural SVMs when Exact Inference Is Intractable,” Proc. Int'l Conf. Machine Learning, 2008.
[41] S. Belongie, J. Malik, and J. Puzicha, “Shape Matching and Object Recognition Using Shape Contexts,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp.509-521, Apr. 2002.
[42] CMU “house” data set, http://vasc.ri.cmu.edu/idb/html/motion/house index.html, 2009.
[43] T.S. Caetano, T. Caelli, D. Schuurmans, and D.A.C. Barone, “Graphical Models and Point Pattern Matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp.1646-1663, Oct. 2006.
[44] A.M. Bronstein, M.M. Bronstein, and R. Kimmel, Numerical Geometry of Non-Rigid Shapes. Springer, 2007.
[45] A.M. Bronstein, M.M. Bronstein, A.M. Bruckstein, and R. Kimmel, “Analysis of Two-Dimensional Non-Rigid Shapes,” Int'l J. Computer Vision, 2007.
[46] Mythological Creatures 2D database, http:/tosca.cs.technion. ac.il, 2009.
[47] SAMPL motion data set, http://sampl.ece.ohio-state.edudatabase.htm , 2009.
[48] S. Smith, “A New Class of Corner Finder,” Proc. British Machine Vision Conf., pp.139-148, 1992.
[49] S. Smith, “Flexible Filter Neighbourhood Designation,” Proc. Int'l Conf. Pattern Recognition, pp.206-212, 1996.
[50] G. Griffin, A. Holub, and P. Perona, “Caltech-256 Object Category Data Set,” Technical Report 7694, California Institute of Tech nology, http://authors.library.caltech.edu7694, 2007.

Index Terms:
Graph matching, Learning, Support Vector Machines, Structured Estimation, Optimization
Citation:
Tibério S. Caetano, Julian J. McAuley, Li Cheng, Quoc V. Le, Alex J. Smola, "Learning Graph Matching," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 6, pp. 1048-1058, June 2009, doi:10.1109/TPAMI.2009.28
Usage of this product signifies your acceptance of the Terms of Use.