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Issue No.09 - Sept. (2013 vol.35)
pp: 2131-2142
Hairong Liu , Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
L. J. Latecki , Dept. of Comput. & Inf. Sci., Temple Univ., Philadelphia, PA, USA
Shuicheng Yan , Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
ABSTRACT
In this paper, we propose an efficient algorithm to detect dense subgraphs of a weighted graph. The proposed algorithm, called the shrinking and expansion algorithm (SEA), iterates between two phases, namely, the expansion phase and the shrink phase, until convergence. For a current subgraph, the expansion phase adds the most related vertices based on the average affinity between each vertex and the subgraph. The shrink phase considers all pairwise relations in the current subgraph and filters out vertices whose average affinities to other vertices are smaller than the average affinity of the result subgraph. In both phases, SEA operates on small subgraphs; thus it is very efficient. Significant dense subgraphs are robustly enumerated by running SEA from each vertex of the graph. We evaluate SEA on two different applications: solving correspondence problems and cluster analysis. Both theoretic analysis and experimental results show that SEA is very efficient and robust, especially when there exists a large amount of noise in edge weights.
INDEX TERMS
Algorithm design and analysis, Clustering algorithms, Vectors, Heuristic algorithms, Robustness, Noise, Indexes,cluster analysis, Dense subgraph, correspondence, point set matching, maximum common subgraph
CITATION
Hairong Liu, L. J. Latecki, Shuicheng Yan, "Fast Detection of Dense Subgraphs with Iterative Shrinking and Expansion", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 9, pp. 2131-2142, Sept. 2013, doi:10.1109/TPAMI.2013.16
REFERENCES
[1] J. Shi and J. Malik, "Normalized Cuts and Image Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 888-905, Aug. 2000.
[2] M. Girvan and M. Newman, "Community Structure in Social and Biological Networks," Proc. Nat'l Academy of Sciences, vol. 99, no. 12, pp. 7821-7826, 2002.
[3] J. Chen and Y. Saad, "Dense Subgraph Extraction with Application to Community Detection," IEEE Trans. Knowledge and Data Eng., vol. 24, no. 7, pp. 1216-1230, July 2012.
[4] Q. Ouyang, P. Kaplan, S. Liu, and A. Libchaber, "DNA Solution of the Maximal Clique Problem," Science, vol. 80, pp. 446-448, 1997.
[5] K. Crammer, P. Talukdar, and F. Pereira, "A Rate-Distortion One-Class Model and Its Applications to Clustering," Proc. Int'l Conf. Machine Learning, pp. 184-191, 2008.
[6] G. Palla, I. Derényi, I. Farkas, and T. Vicsek, "Uncovering the Overlapping Community Structure of Complex Networks in Nature and Society," Nature, vol. 435, no. 7043, pp. 814-818, 2005.
[7] A. Clauset, M. Newman, and C. Moore, "Finding Community Structure in Very Large Networks," Physical Rev. E, vol. 70, no. 6, pp. 66-71, 2004.
[8] M. Zaki, S. Parthasarathy, M. Ogihara, and W. Li, "New Algorithms for Fast Discovery of Association Rules," Proc. Int'l Conf. Knowledge Discovery and Data Mining, vol. 20, pp. 283-286, 1997.
[9] T. Motzkin and E. Straus, "Maxima for Graphs and a New Proof of a Theorem of Turán," Canadian J. Math., vol. 17, no. 4, pp. 533-540, 1965.
[10] M. Pavan and M. Pelillo, "Dominant Sets and Pairwise Clustering," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 1, pp. 167-172, Jan. 2007.
[11] D. Comaniciu and P. Meer, "Mean Shift: A Robust Approach toward Feature Space Analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 5, pp. 603-619, May 2002.
[12] I. Bomze, "Branch-and-Bound Approaches to Standard Quadratic Optimization Problems," J. Global Optimization, vol. 22, no. 1, pp. 17-37, 2002.
[13] H. Kuhn and A. Tucker, "Nonlinear Programming," Proc. Berkeley Symp. Math. Statistics and Probability, pp. 481-492, 1951.
[14] J. Weibull, Evolutionary Game Theory. The MIT Press, 1997.
[15] J. Maciel and J. Costeira, "A Global Solution to Sparse Correspondence Problems," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 187-199, Feb. 2003.
[16] T. Caetano, T. Caelli, D. Schuurmans, and D. Barone, "Graphical Models and Point Pattern Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1646-1663, Oct. 2006.
[17] H. Jiang, M. Drew, and Z. Li, "Matching by Linear Programming and Successive Convexification," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 959-975, June 2007.
[18] B. Georgescu and P. Meer, "Point Matching under Large Image Deformations and Illumination Changes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 6, pp. 674-688, June 2004.
[19] A. Cross and E. Hancock, "Graph Matching with a Dual-Step EM Algorithm," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 11, pp. 1236-1253, Nov. 1998.
[20] M. Zaslavskiy, F. Bach, and J. Vert, "A Path Following Algorithm for the Graph Matching Problem," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 12, pp. 2227-2242, Dec. 2009.
[21] R. Horaud and T. Skordas, "Stereo Correspondence through Feature Grouping and Maximal Cliques," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 11, pp. 1168-1180, Nov. 1989.
[22] M. Pelillo, "Matching Free Trees with Replicator Equations," Proc. Advances in Neural Information Processing Systems Conf., pp. 865-872, 2002.
[23] A. Albarelli, S. Bulo, and M. Pelillo, "Matching as a Non-Cooperative Game," Proc. IEEE Int'l Conf. Computer Vision, 2009.
[24] M. Leordeanu and M. Hebert, "A Spectral Technique for Correspondence Problems Using Pairwise Constraints," Proc. IEEE Int'l Conf. Computer Vision, pp. 1482-1489, 2005.
[25] M. Leordeanu, M. Hebert, and R. Sukthankar, "An Integer Projected Fixed Point Method for Graph Matching and Map Inference," Proc. Advances in Neural Information Processing Systems Conf., vol. 1, no. 3, p. 4, 2009.
[26] O. Duchenne, F. Bach, I. Kweon, and J. Ponce, "A Tensor-Based Algorithm for High-Order Graph Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1980-1987, 2009.
[27] M. Cho, J. Lee, and K. Lee, "Reweighted Random Walks for Graph Matching," Proc. European Conf. Computer Vision, pp. 492-505, 2010.
[28] R. Zass and A. Shashua, "Probabilistic Graph and Hypergraph Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2008.
[29] J. Zhu, S. Hoi, M. Lyu, and S. Yan, "Near-Duplicate Keyframe Retrieval by Nonrigid Image Matching," Proc. ACM Int'l Conf. Multimedia, pp. 41-50, 2008.
[30] D. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int'l J. Computer Vision, vol. 60, no. 2, pp. 91-110, 2004.
[31] X. Wu, W. Zhao, and C. Ngo, "Near-Duplicate Keyframe Retrieval with Visual Keywords and Semantic Context," Proc. ACM Int'l Conf. Image and Video Retrieval, pp. 169-176, 2007.
[32] W. Zhao, C. Ngo, H. Tan, and X. Wu, "Near-Duplicate Keyframe Identification with Interest Point Matching and Pattern Learning," IEEE Trans. Multimedia, vol. 9, no. 5, pp. 1037-1048, Aug. 2007.
[33] D. Conte, C. Guidobaldi, and C. Sansone, "A Comparison of Three Maximum Common Subgraph Algorithms on a Large Database of Labeled Graphs," Proc. Fourth IAPR Int'l Conf. Graph Based Representations in Pattern Recognition, vol. 2726, pp. 130-141, 2003.
[34] P. Durand, R. Pasari, J. Baker, and C. Tsai, "An Efficient Algorithm for Similarity Analysis of Molecules," Int'l J. Chemistry, vol. 2, no. 17, pp. 1-16, 1999.
[35] T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, "An Efficient K-Means Clustering Algorithm: Analysis and Implementation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 7, pp. 881-892, July 2002.
[36] A. Ng, M. Jordan, and Y. Weiss, "On Spectral Clustering: Analysis and an Algorithm," Proc. Advances in Neural Information Processing Systems Conf., vol. 2, pp. 849-856, 2002.
[37] H. Ling and D. Jacobs, "Shape Classification Using the Inner-Distance," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 2, pp. 286-299, Feb. 2007.
[38] B. Frey and D. Dueck, "Clustering by Passing Messages between Data Points," Science, vol. 315, no. 5814, pp. 972-976, 2007.
[39] F. Lin and W. Cohen, "Power Iteration Clustering," Proc. Int'l Conf. Machine Learning, 2010.
[40] M. Hein and T. Bühler, "An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA," Proc. Advances in Neural Information Processing Systems Conf., 2010.
[41] S. Bulò and M. Pelillo, "A Game-Theoretic Approach to Hypergraph Clustering," Proc. Advances in Neural Information Processing Systems Conf., vol. 22, pp. 1571-1579, 2009.
[42] H. Liu, L. Latecki, and S. Yan, "Robust Clustering as Ensembles of Affinity Relations," Proc. Advances in Neural Information Processing Systems, 2010.
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