Graph-Based Relational Learning with a Polynomial Time Projection Algorithm

  • Brahim Douar
  • Michel Liquiere
  • Chiraz Latiri
  • Yahya Slimani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7207)


The paper presents a new projection operator, named AC- projection, which exhibits good complexity properties as opposed to the graph isomorphism operator typically used in graph mining. We study the size and structure of the search space and some practical properties of the projection operator. These properties give us a specialization algorithm using simple local operations. Then we prove experimentally that we can achieve an important performance gain without or with non-significant loss of discovered patterns quality.


Projection operator Specialization algorithm Relational learning Structural description Graph classification 


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  1. 1.
    Bessière, C., Régin, J.-C.: Mac and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 61–75. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  2. 2.
    Cook, D.J., Holder, L.B.: Mining Graph Data. John Wiley & Sons (2006)Google Scholar
  3. 3.
    Debnath, A., Compadre, R.D., Debnath, G., Schusterman, A., Hansch, C.: Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. Correlation with molecular orbital energies and hydrophobicity. J. Medicinal Chemistry 34 (1991)Google Scholar
  4. 4.
    Hell, P., Nesetril, J.: Graphs and homomorphism, vol. 28. Oxford University Press, Oxford (2004)CrossRefGoogle Scholar
  5. 5.
    Helma, C., King, R.D., Kramer, S., Srinivasan, A.: The predictive toxicology challenge 2000-2001. Bioinformatics 17(1), 107–108 (2001)CrossRefGoogle Scholar
  6. 6.
    Kuramochi, M., Karypis, G.: Frequent subgraph discovery. In: Cercone, N., Lin, T.Y., Wu, X. (eds.) International Conference on Data Mining, pp. 313–320. IEEE Computer Society (2001)Google Scholar
  7. 7.
    Liquiere, M.: Arc Consistency Projection: A New Generalization Relation for Graphs. In: Priss, U., Polovina, S., Hill, R. (eds.) ICCS 2007. LNCS (LNAI), vol. 4604, pp. 333–346. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Malerba, D., Lisi, F.A.: Discovering Associations between Spatial Objects: An ILP Application. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 156–163. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Nienhuys-Cheng, S.H., de Wolf, R.: Least generalizations and greatest specializations of sets of clauses. CoRR cs.AI/9605102 (1996)Google Scholar
  10. 10.
    Plotkin, G.D.: A note on inductive generalization. Machine Intelligence 5 (1970)Google Scholar
  11. 11.
    Provost, F.J., Fawcett, T.: Robust Classification for Imprecise Environments. Machine Learning 42(3), 203–231 (2001)zbMATHCrossRefGoogle Scholar
  12. 12.
    Quinlan, J.R.: C4.5: Programs for Machine Learning, 1st edn. Morgan Kaufmann (January 1993)Google Scholar
  13. 13.
    Sowa, J.F.: Conceptual graphs summary, pp. 3–51. Ellis Horwood (1992)Google Scholar
  14. 14.
    Wessel, M.D., Jurs, P.C., Tolan, J.W., Muskal, S.M.: Prediction of human intestinal absorption of drug compounds from molecular structure. Journal of Chemical Information and Computer Sciences 38(4), 726–735 (1998)CrossRefGoogle Scholar
  15. 15.
    Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques, 2nd edn. Morgan Kaufmann Series in Data Management Systems. Morgan Kaufmann Publishers Inc., San Francisco (2005)zbMATHGoogle Scholar
  16. 16.
    Wörlein, M., Meinl, T., Fischer, I., Philippsen, M.: A Quantitative Comparison of the Subgraph Miners MoFa, gSpan, FFSM, and Gaston. In: Jorge, A.M., Torgo, L., Brazdil, P.B., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 392–403. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Yan, X., Han, J.: gspan: Graph-based substructure pattern mining. In: International Conference on Data Mining, pp. 721–724. IEEE Computer Society (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Brahim Douar
    • 1
    • 2
  • Michel Liquiere
    • 1
    • 3
  • Chiraz Latiri
    • 2
  • Yahya Slimani
    • 2
  1. 1.LIRMMMontpellierFrance
  2. 2.URPAH TeamFaculty of Sciences of TunisTunisia
  3. 3.IUT BéziersFrance

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