Skip to main content
SpringerLink
Log in

Attributed graph mining in the presence of automorphism

  • Regular Paper
  • Published:
Knowledge and Information Systems Aims and scope Submit manuscript

Abstract

Attributed directed graphs are directed graphs in which nodes are associated with sets of attributes. Many data from the real world can be naturally represented by this type of structure, but few algorithms are able to directly handle these complex graphs. Mining attributed graphs is a difficult task because it requires combining the exploration of the graph structure with the identification of frequent itemsets. In addition, due to the combinatorics on itemsets, subgraph isomorphisms (which have a significant impact on performances) are much more numerous than in labeled graphs. In this paper, we present a new data mining method that can extract frequent patterns from one or more directed attributed graphs. We show how to reduce the combinatorial explosion induced by subgraph isomorphisms thanks to an appropriate processing of automorphic patterns.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. Graphs with labeled edges can always be transformed into graphs with only labels on nodes (using, e.g., the method proposed by [11]). For this reason, we only consider attributed nodes in our study.

References

  1. Agrawal R, Imieliński T, Swami A (1993) Mining association rules between sets of items in large databases. SIGMOD Rec 22(2):207–216

    Article  Google Scholar 

  2. Agrawal R, Srikant R (1995) Mining sequential patterns. In: ICDE’95, pp 3–14

  3. Ayres J, Flannick J, Gehrke J, Yiu T (2002) Sequential pattern mining using a bitmap representation. In: KDD’02, pp 429–435

  4. Borgelt C (2007) Canonical forms for frequent graph mining. In: Decker R, Lenz H-J (eds) Advances in data analysis. Springer, Berlin, pp 337–349

    Chapter  Google Scholar 

  5. Borgelt C, Berthold M (2002) Mining molecular fragments: finding relevant substructures of molecules. In: ICDM’02, pp 51–58

  6. Bringmann B, Nijssen S (2008) What is frequent in a single graph?. In: PAKDD’08, pp 858–863

  7. Chi Y, Yang Y, Xia Y, Muntz RR (2004) Cmtreeminer: mining both closed and maximal frequent subtrees. In: PAKDD’04, pp 63–73

  8. Fukuzaki M, Seki M, Kashima H, Sese J (2010) Finding itemset-sharing patterns in a large itemset-associated graph. In: PAKDD’10, pp 147–159

  9. Huan J, Wang W, Prins J (2003) Efficient mining of frequent subgraphs in the presence of isomorphism. In: ICDM’05, pp 549–552

  10. Inokuchi A, Washio T, Motoda H (2000) An apriori-based algorithm for mining frequent substructures from graph data. In: PKDD’00, pp 13–23

  11. Inokuchi A, Washio T, Motoda H (2003) Complete mining of frequent patterns from graphs: mining graph data. Mach Learn 50(3):321–354

    Article  MATH  Google Scholar 

  12. Jiang C, Coenen F, Zito M (2013) A survey of frequent subgraph mining algorithms. Knowl Eng Rev 28:75–105

    Article  Google Scholar 

  13. Johnsonbaugh R, Kalin M (1991) A graph generation software package. SIGCSE Bull 23(1):151–154

    Article  Google Scholar 

  14. Kuramochi M, Karypis G (2001) Frequent subgraph discovery. In: ICDM’01, pp 313–320

  15. Kuramochi M, Karypis G (2004) An efficient algorithm for discovering frequent subgraphs. IEEE Trans Knowl Data Eng 16(9):1038–1051

    Article  Google Scholar 

  16. Mannila H, Toivonen H (2005) Multiple uses of frequent sets and condensed representations. In: KDD’05, pp 189–194

  17. McAuley J, Leskovec J (2012) Learning to discover social circles in ego networks. Neural Inf Process Syst 25:548–556

    Google Scholar 

  18. Miyoshi Y, Ozaki T, Ohkawa T (2009) Frequent pattern discovery from a single graph with quantitative itemsets. In: ICDMW’09, pp 527–532

  19. Pasquier C, Sanhes J, Flouvat F, Selmaoui-Folcher N (2015) Frequent pattern mining in attributed trees: algorithms and applications. Knowl Inf Syst 46(3):491–514

    Article  Google Scholar 

  20. Pasquier N, Bastide Y, Taouil R, Lakhal L (1999) Discovering frequent closed itemsets for association rules. In: ICDT’99, pp 398–416

  21. Wörlein M, Meinl T, Fischer I, Philippsen M (2005) A quantitative comparison of the subgraph miners mofa, gspan, ffsm, and gaston. In: PKDD’05, pp 392–403

  22. Yan X, Han J (2002) gspan: graph-based substructure pattern mining. In: ICDM’02, pp 721–724

  23. Yan X, Han J (2003) CloseGraph: mining closed frequent graph patterns. In: KDD’03, pp 286–295

  24. Yan X, Yu PS, Han J (2004) Graph indexing: a frequent structure-based approach. In: SIGMOD conference, pp 335–346

Download references

Acknowledgments

This work was supported by the ANR Grant “FOSTER” ANR-2010-COSI-012-01.

Author information

Authors and Affiliations

  1. Univ. Nice Sophia Antipolis, I3S, UMR 7271, 06900, Sophia Antipolis, France

    Claude Pasquier

  2. CNRS, I3S, UMR 7271, 06900, Sophia Antipolis, France

    Claude Pasquier

  3. Multidisciplinary Research Team on Material and Environment (PPME), University of New Caledonia, 98851, Nouméa, New Caledonia

    Claude Pasquier, Frédéric Flouvat, Jérémy Sanhes & Nazha Selmaoui-Folcher

Authors
  1. Claude Pasquier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frédéric Flouvat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jérémy Sanhes
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nazha Selmaoui-Folcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claude Pasquier.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pasquier, C., Flouvat, F., Sanhes, J. et al. Attributed graph mining in the presence of automorphism. Knowl Inf Syst 50, 569–584 (2017). https://doi.org/10.1007/s10115-016-0953-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10115-016-0953-9

Keywords

Search

Navigation