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Fast Detection of Dense Subgraphs with Iterative Shrinking and Expansion
Sept. 2013 (vol. 35 no. 9)
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
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:
object detection,graph theory,iterative methods,cluster analysis,dense subgraph detection,iterative shrinking,weighted graph,shrinking and expansion algorithm,SEA,expansion phase,shrink phase,correspondence problems,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 and Machine Intelligence, vol. 35, no. 9, pp. 2131-2142, Sept. 2013, doi:10.1109/TPAMI.2013.16
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