Skip to main content

Advertisement

SpringerLink
Log in

Relational concept analysis: mining concept lattices from multi-relational data

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

The processing of complex data is admittedly among the major concerns of knowledge discovery from data (kdd). Indeed, a major part of the data worth analyzing is stored in relational databases and, since recently, on the Web of Data. This clearly underscores the need for Entity-Relationship and rdf compliant data mining (dm) tools. We are studying an approach to the underlying multi-relational data mining (mrdm) problem, which relies on formal concept analysis (fca) as a framework for clustering and classification. Our relational concept analysis (rca) extends fca to the processing of multi-relational datasets, i.e., with multiple sorts of individuals, each provided with its own set of attributes, and relationships among those. Given such a dataset, rca constructs a set of concept lattices, one per object sort, through an iterative analysis process that is bound towards a fixed-point. In doing that, it abstracts the links between objects into attributes akin to role restrictions from description logics (dls). We address here key aspects of the iterative calculation such as evolution in data description along the iterations and process termination. We describe implementations of rca and list applications to problems from software and knowledge engineering.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adda, M., Valtchev, P., Djeraba, C., Missaoui, R.: Toward recommendation based on ontology-powered web-usage mining. IEEE Internet Computing 11(4):45–52 (2007)

    Article  Google Scholar 

  2. Agrawal, R., Srikant, R.: Mining sequential patterns. In: Proceedings of the 11th Intl. Conf. on Data Engineering (ICDE’95), pp. 3–14. IEEE Computer Society (1995)

  3. Arévalo, G., Falleri, J.-R., Huchard, M., Nebut, C.: Building abstractions in class models: formal concept analysis in a model-driven approach. In: Nierstrasz, O., Whittle, J., Harel, D., Reggio, G. (eds.) Proc. of the 9th Intl. Conf. MoDELS. LNCS, vol. 4199, pp. 513–527. Springer (2006)

  4. Azmeh, Z., Driss, M., Hamoui, F., Huchard, M., Moha, N., Tibermacine, C.: Selection of composable web services driven by user requirements. In: ICWS, pp. 395–402. IEEE Computer Society (2011)

  5. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  6. Barbut, M., Monjardet, B.: Ordre et Classification: Algèbre et Combinatoire, vol. 2. Hachette (1970)

  7. Belohlavek, R.: Concept lattices and order in fuzzy logic. Ann. Pure Appl. Logic 128, 277–298 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bendaoud, R., Napoli, A., Toussaint, Y.: Formal concept analysis: a unified framework for building and refining ontologies. In: Gangemi, A., Euzenat, J. (eds.) Knowledge Engineering: Practice and Patterns, Proc. of the 16th Intl. Conf. EKAW, LNCS 5268, pp. 156–171 (2008)

  9. Cook, D., Holder, L.: Mining Graph Data. Wiley-Interscience (2006)

  10. De Raedt, L.: Logical and Relational Learning (Cognitive Technologies), 1st edn. Springer (2008)

  11. Dehaspe, L., Toivonen, H.: Discovery of frequent datalog patterns. Data Mining and Knowledge Discovery 3, 7–36 (1999)

    Article  Google Scholar 

  12. Džeroski, S.: Multi-relational data mining: an introduction. SIGKDD Explor. Newsl. 5, 1–16 (2003)

    Article  Google Scholar 

  13. Džeroski, S., Lavrac, N. (eds.): Relational Data Mining. Springer (2001)

  14. Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.): Advances in Knowledge Discovery and Data Mining. AAAI/MIT Press (1996)

  15. Ferré, S., Ridoux, O., Sigonneau, B.: Arbitrary relations in formal concept analysis and logical information systems. In: Mugnier, M.-L., Dau, F., Stumme, G. (eds.) Proc. of the 13th Intl. Conf. on Conceptual Structures (ICCS’05), Kassel, Germany. LNCS, vol. 3596, pp. 166–180. Springer (2005)

  16. Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer (1999)

  17. Huchard, M., Rouane-Hacene, M., Roume, C., Valtchev, P.: Relational concept discovery in structured datasets. Ann. Math. Artif. Intell. 49(1–4), 39–76 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kuznetsov, S.O.: Learning of simple conceptual graphs from positive and negative examples. In: Zytkow, J.M., Rauch, J. (eds.) Proc. of the Third European Conf. PKDD’99, Prague, Czech Republic, vol. 1704, pp. 384–391 (1999)

  19. Kuznetsov, S.O., Obiedkov, S.A.: Comparing the performance of algorithms for generating concept lattices. J. Exp. Theor. Artif. Intell. 14(2–3), 189–216 (2002)

    Article  MATH  Google Scholar 

  20. Lehmann, J., Hitzler, P.: Concept learning in description logics using refinement operators. Mach. Learn. 78, 203–250 (2010)

    Article  Google Scholar 

  21. Liquière, M., Sallantin, J.: Structural machine learning with Galois lattice and graphs. In: Proc. of the 15th Intl. Conf. on Machine Learning (ICML’98), pp. 305–313 (1998)

  22. Mann, R.D., Andrews, E.B. (eds.): Pharmacovigilance. Wiley (2002)

  23. Moha, N., Rouane-Hacene, M., Valtchev, P., Guéhéneuc, Y.-G.: Refactorings of design defects using relational concept analysis. In: Medina, R., Obiedkov, S. (eds.) Proc. of the 6th Intl. Conf. on Formal Concept Analysis (ICFCA’08). LNCS, vol. 4933, pp. 289–304. Springer (2008)

  24. Prediger, S., Stumme, G.: Theory-driven logical scaling. In: Proc. 6th Intl. Workshop Knowledge Representation Meets Databases, Heidelberg. CEUR Workshop Proc., pp. 46–49 (1999)

  25. Prediger, S., Wille, R.: The lattice of concept graphs of a relationally scaled context. In: Proc. of the 7th Intl. Conf. on Conceptual Structures (ICCS’99), pp. 401–414. Springer (1999)

  26. Priss, U.: Efficient implementation of semantic relations in lexical databases. Comput. Intell. 15, 79–87 (1999)

    Article  Google Scholar 

  27. Rouane-Hacene, M., Huchard, M., Napoli, A., Valtchev, P.: A proposal for combining formal concept analysis and description logics for mining relational data. In: Kuznetsov, S., Schmidt, S. (eds.) Proc. of the 5th Intl. Conf. on Formal Concept Analysis (ICFCA’07). LNCS, vol. 4390, pp. 51–65. Springer (2007)

  28. Rouane-Hacene, M., Valtchev, P., Nkambou, R.: Supporting ontology design through large-scale FCA-based ontology restructuring. In: Proc. of the 19th International Conference on Conceptual Structures, ICCS 2011—Conceptual Structures for Discovering Knowledge—, Derby, UK, 25–29 July 2011, pp. 257–269 (2011)

  29. Rudolph, S.: Exploring relational structures via FLE. In: Pfeiffer, H.D., Wolff, K.E., Delugach, H.S. (eds.) Proc. of the 12th Intl. Conf. on Conceptual Structures, ICCS 2004, Huntsville (AL). LNAI, vol. 3127, pp. 196–212. Springer, Berlin (2004)

    Google Scholar 

  30. Saada, H., Dolques, X., Huchard, M., Nebut, C., Sahraoui, H.A.: Generation of operational transformation rules from examples of model transformations. In: France, R., Kazmeier, J., Breu, R., Atkinson, C. (eds.) Proc. 15th Intl. Conf. MODELS’12, Innsbruck (AT). Lecture Notes in Computer Science, vol. 7590, pp. 546–561. Springer (2012)

  31. Shi, L., Toussaint, Y., Napoli, A., Blansché, A.: Mining for reengineering: an application to semantic wikis using formal and relational concept analysis. In: Antoniou, G., Grobelnik, M., Simperl, E., Parsia, B., Plexousakis, D., Pan, J., De Leenheer, P. (eds.) Proc. of the 8th Extended Semantic Web Conf. (ESWC’11). LNCS, vol. 6644, pp. 421–435. Springer (2011)

  32. Srikant, R., Agrawal, R.: Mining generalized association rules. In: Proc. of the 21st Intl. Conf. on Very Large Databases (VLDB’95), Zurich (CH) (1995)

  33. Valtchev, P., Missaoui, R., Lebrun, P.: A partition-based approach towards building Galois (concept) lattices. Discrete Math. 256(3), 801–829 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Valtchev, P., Rouane-Hacene, M., Missaoui, R.: A generic scheme for the design of efficient on-line algorithms for lattices. In: de Moor, A., Lex, W., Ganter, B. (eds.) Proc. of the 11th Intl. Conf. on Conceptual Structures (ICCS’03). LNCS, vol. 2746, pp. 282–295. Springer (2003)

  35. Valtchev, P., Missaoui, R., Godin, R.: Formal concept analysis for knowledge discovery and data mining: the new challenges. In: Eklund, P. (ed.) Proc. of the 2nd Intl. Conf. on Formal Concept Analysis (ICFCA’04), Sydney (AU). LNCS, vol. 2961, pp. 352–371. Springer (2004)

  36. Washio, T., Motoda, H.: State of the art of graph-based data mining. SIGKDD Explor. Newsl. 5(1), 59–68 (2003)

    Article  Google Scholar 

  37. Wille, R.: Restructuring the lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht-Boston (1982)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dépt. Informatique, UQÀM, CP 8888, succ. CV, Montréal, Canada, H3C 3P8

    Mohamed Rouane-Hacene & Petko Valtchev

  2. LIRMM (CNRS – Université de Montpellier), 161 rue Ada, 34095, Montpellier Cedex 5, France

    Marianne Huchard

  3. LORIA (CNRS – INRIA – Université de Lorraine), B.P. 239, 54506, Vandœuvre-lès-Nancy, France

    Amedeo Napoli

Authors
  1. Mohamed Rouane-Hacene
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marianne Huchard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amedeo Napoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Petko Valtchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Rouane-Hacene.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rouane-Hacene, M., Huchard, M., Napoli, A. et al. Relational concept analysis: mining concept lattices from multi-relational data. Ann Math Artif Intell 67, 81–108 (2013). https://doi.org/10.1007/s10472-012-9329-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-012-9329-3

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation