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Mining Large Information Networks by Graph Summarization

  • Chen Chen
  • Cindy Xide Lin
  • Matt Fredrikson
  • Mihai Christodorescu
  • Xifeng Yan
  • Jiawei Han
Chapter

Abstract

Graphs are prevalent in many domains such as bioinformatics, social networks, Web, and cybersecurity. Graph pattern mining has become an important tool in the management and analysis of complexly structured data, where example applications include indexing, clustering, and classification. Existing graph mining algorithms have achieved great success by exploiting various properties in the pattern space. Unfortunately, due to the fundamental role subgraph isomorphism plays in these methods, they may all enter into a pitfall when the cost to enumerate a huge set of isomorphic embeddings blows up, especially in large graphs. The solution we propose for this problem resorts to reduction on the data space. For each graph, we build a summary of it and mine this shrunk graph instead. Compared to other data reduction techniques that either reduce the number of transactions or compress between transactions, this new framework, called Summarize-Mine, suggests a third path by compressing within transactions. Summarize-Mine is effective in cutting down the size of graphs, thus decreasing the embedding enumeration cost. However, compression might lose patterns at the same time. We address this issue by generating randomized summaries and repeating the process for multiple rounds, where the main idea is that true patterns are unlikely to miss from all rounds. We provide strict probabilistic guarantees on pattern loss likelihood. Experiments on real malware trace data show that Summarize-Mine is very efficient, which can find interesting malware fingerprints that were not revealed previously.

References

  1. 1.
    R. Agrawal and R. Srikant. Fast algorithms for mining association rules in large databases. In VLDB, pages 487–499, 1994.Google Scholar
  2. 2.
    D. Chakrabarti and C. Faloutsos. Graph mining: Laws, generators, and algorithms. ACM Computing Survey, 38(1):1–69, 2006.CrossRefGoogle Scholar
  3. 3.
    C. Chen, X. Yan, F. Zhu, J. Han, and P. S. Yu. Graph OLAP: Towards online analytical processing on graphs. In ICDM, pages 103–112, 2008.Google Scholar
  4. 4.
    J. Chen, W. Hsu, M.-L. Lee, and S.-K. Ng. Nemofinder: Dissecting genome-wide protein-protein interactions with meso-scale network motifs. In KDD, pages 106–115, 2006.Google Scholar
  5. 5.
    M. Christodorescu, S. Jha, and C. Kruegel. Mining specifications of malicious behavior. In ESEC/SIGSOFT FSE, pages 5–14, 2007.Google Scholar
  6. 6.
    M. Deshpande, M. Kuramochi, N. Wale, and G. Karypis. Frequent substructure-based approaches for classifying chemical compounds. IEEE Transactions on Knowledge and Data Engineering, 17(8):1036–1050, 2005.CrossRefGoogle Scholar
  7. 7.
    M. N. Garofalakis and P. B. Gibbons. Approximate query processing: Taming the terabytes (tutorial). In VLDB, 2001.Google Scholar
  8. 8.
    J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. In SIGMOD Conference, pages 1–12, 2000.Google Scholar
  9. 9.
    M. A. Hasan, V. Chaoji, S. Salem, J. Besson, and M. J. Zaki. Origami: Mining representative orthogonal graph patterns. In ICDM, pages 153–162, 2007.Google Scholar
  10. 10.
    H. He and A. K. Singh. Efficient algorithms for mining significant substructures in graphs with quality guarantees. In ICDM, pages 163–172, 2007.Google Scholar
  11. 11.
    L. B. Holder, D. J. Cook, and S. Djoko. Substucture discovery in the subdue system. In KDD Workshop, pages 169–180, 1994.Google Scholar
  12. 12.
    J. Huan, W. Wang, J. Prins, and J. Yang. Spin: Mining maximal frequent subgraphs from graph databases. In KDD, pages 581–586, 2004.Google Scholar
  13. 13.
    A. Inokuchi, T. Washio, and H. Motoda. Complete mining of frequent patterns from graphs: Mining graph data. Machine Learning, 50(3):321–354, 2003.CrossRefGoogle Scholar
  14. 14.
    S. Kramer, L. De Raedt, and C. Helma. Molecular feature mining in hiv data. In KDD, pages 136–143, 2001.Google Scholar
  15. 15.
    M. Kuramochi and G. Karypis. Frequent subgraph discovery. In ICDM, pages 313–320, 2001.Google Scholar
  16. 16.
    M. Kuramochi and G. Karypis. Finding frequent patterns in a large sparse graph. Data Mining and Knowledge Discovery, 11(3):243–271, 2005.CrossRefGoogle Scholar
  17. 17.
    A. Lachmann and M. Riedewald. Finding relevant patterns in bursty sequences. PVLDB, 1(1):78–89, 2008.Google Scholar
  18. 18.
    J. Leskovec, J. M. Kleinberg, and C. Faloutsos. Graphs over time: Densification laws, shrinking diameters and possible explanations. In KDD, pages 177–187, 2005.Google Scholar
  19. 19.
    S. Navlakha, R. Rastogi, and N. Shrivastava. Graph summarization with bounded error. In SIGMOD Conference, pages 419–432, 2008.Google Scholar
  20. 20.
    J. Pei, D. Jiang, and A. Zhang. On mining cross-graph quasi-cliques. In KDD, pages 228–238, 2005.Google Scholar
  21. 21.
    N. Polyzotis and M. N. Garofalakis. Xsketch synopses for xml data graphs. ACM Transactions on Database Systems, 31(3):1014–1063, 2006.CrossRefGoogle Scholar
  22. 22.
    S. Raghavan and H. Garcia-Molina. Representing web graphs. In ICDE, pages 405–416, 2003.Google Scholar
  23. 23.
    S. Reinhardt and G. Karypis. A multi-level parallel implementation of a program for finding frequent patterns in a large sparse graph. In IPDPS, pages 1–8, 2007.Google Scholar
  24. 24.
    T. Sarlós, A. A. Benczúr, K. Csalogány, D. Fogaras, and B. Rácz. To randomize or not to randomize: Space optimal summaries for hyperlink analysis. In WWW, pages 297–306, 2006.Google Scholar
  25. 25.
    Y. Tian, R. A. Hankins, and J. M. Patel. Efficient aggregation for graph summarization. In SIGMOD Conference, pages 567–580, 2008.Google Scholar
  26. 26.
    H. Toivonen. Sampling large databases for association rules. In VLDB, pages 134–145, 1996.Google Scholar
  27. 27.
    X. Yan, H. Cheng, J. Han, and P. S. Yu. Mining significant graph patterns by leap search. In SIGMOD Conference, pages 433–444, 2008.Google Scholar
  28. 28.
    X. Yan and J. Han. gSpan: Graph-based substructure pattern mining. In ICDM, pages 721–724, 2002.Google Scholar
  29. 29.
    X. Yan, P. S. Yu, and J. Han. Graph indexing: A frequent structure-based approach. In SIGMOD Conference, pages 335–346, 2004.Google Scholar
  30. 30.
    N. Zhang, V. Kacholia, and M. T. Özsu. A succinct physical storage scheme for efficient evaluation of path queries in xml. In ICDE, pages 54–65, 2004.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Chen Chen
    • 1
  • Cindy Xide Lin
    • 1
  • Matt Fredrikson
    • 2
  • Mihai Christodorescu
    • 3
  • Xifeng Yan
    • 4
  • Jiawei Han
    • 5
  1. 1.University of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.University of Wisconsin at MadisonMadisonUSA
  3. 3.IBM T. J. Watson Research CenterHawthorneUSA
  4. 4.University of California at Santa BarbaraSanta BarbaraUSA
  5. 5.UIUCUrbanaUSA

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