Skip to main content

Advertisement

SpringerLink
Log in

Relational concept discovery in structured datasets

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

Abstract

Relational datasets, i.e., datasets in which individuals are described both by their own features and by their relations to other individuals, arise from various sources such as databases, both relational and object-oriented, knowledge bases, or software models, e.g., UML class diagrams. When processing such complex datasets, it is of prime importance for an analysis tool to hold as much as possible to the initial format so that the semantics is preserved and the interpretation of the final results eased. Therefore, several attempts have been made to introduce relations into the formal concept analysis field which otherwise generated a large number of knowledge discovery methods and tools. However, the proposed approaches invariably look at relations as an intra-concept construct, typically relating two parts of the concept description, and therefore can only lead to the discovery of coarse-grained patterns. As an approach towards the discovery of finer-grain relational concepts, we propose to enhance the classical (object × attribute) data representations with a new dimension that is made out of inter-object links (e.g., spouse, friend, manager-of, etc.). Consequently, the discovered concepts are linked by relations which, like associations in conceptual data models such as the entity-relation diagrams, abstract from existing links between concept instances. The borders for the application of the relational mining task are provided by what we call a relational context family, a set of binary data tables representing individuals of various sorts (e.g., human beings, companies, vehicles, etc.) related by additional binary relations. As we impose no restrictions on the relations in the dataset, a major challenge is the processing of relational loops among data items. We present a method for constructing concepts on top of circular descriptions which is based on an iterative approximation of the final solution. The underlying construction methods are illustrated through their application to the restructuring of class hierarchies in object-oriented software engineering, which are described in UML.

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. Barbutm, M., Monjardet, B.: Ordre et Classification: Algèbre et combinatoire. Hachette, Paris (1970)

    Google Scholar 

  2. Booch, G., Rumbaugh, J., Jacobson, I.: Unified Modeling Language User Guide. Addison-Wesley, Reading, MA (1999)

    Google Scholar 

  3. Booch, G., Rumbaugh, J., Jacobson, I.: The unified modeling language user guide. In: Object Technology. Addison-Wesley, Reading, MA (2000)

    Google Scholar 

  4. Chaudron, L., Maille, N.: First order logic formal concept analysis: from logic programming to theory. ACIS Int. J. Comput. Inf. Sci. 13(3) (1998)

  5. Chen, P.: The entity-relationship model – toward a unified view of data. ACM Trans. Database Syst. 1(1), 9–36 (1976)

    Article  Google Scholar 

  6. Dao, M.: Validation sur de grands projets, Projet MACAO (RNTL). Technical Report sous-projet MACAO 5.1, France Télécom R&D (December 2003)

  7. Dao, M., Huchard, M., Libourel, T., Roume, C.: Spécification de la prise en compte plus détaillée des éléments du modèle objet UML. Technical report, Projet MACAO. Réseau RNTL (2001)

  8. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge, UK (1992)

    Google Scholar 

  9. Dicky, H., Dony, C., Huchard, M., Libourel, T.: On automatic class insertion with overloading. In: Special issue of Sigplan Notice – Proceedings of ACM OOPSLA’96, pp. 251–267 (1996)

  10. Diday, E., Emillion, R.: Treillis de Galois maximaux et capacités de Choquet. C. R. Acad. Sci. Paris 325(1), 261–266 (1997)

    MATH  Google Scholar 

  11. Džeroski, S., Lavrač, N.: Relational Data Mining. Springer, Berlin Heidelberg New York (2001)

    Google Scholar 

  12. Faid, M., Missaoui, R., Godin, R.: Knowledge discovery in complex objects. Comput. Intell. 15(1), 28–49 (1999)

    Article  Google Scholar 

  13. Ganter, B., Wille, R.: Applications of combinatorics and graph theory to the biological and social sciences. In: The IMA volumes in Mathematics and its applications, chapter Conceptual Scaling, vol. 17, pp. 139–167. Springer, New York (1989)

    Google Scholar 

  14. Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Berlin Heidelberg New York (1999)

    MATH  Google Scholar 

  15. Godin, R., Mili, H.: Building and maintaining analysis-level class hierarchies using Galois lattices. In: Proceedings of OOPSLA’93, Washington (DC), USA, pp. 394–410 (1993)

  16. Godin, R., Mili, H., Mineau, G., Missaoui, R., Arfi, A., Chau, T.T.:Design of class hierarchies based on concept (Galois) lattices. Theory Pract. Object Syst. 4(2), 117–134 (1998)

    Article  Google Scholar 

  17. Polaillon, G., Diday, E.: Symbolic galois lattices of multivariate and interval tables. In: Proceedings of the International Conference on Ordinal and Symbolic Data Analysis (OSDA 97), Darmstadt (1997)

  18. Huchard, M., Dicky, H., Leblanc, H.: Galois lattice as a framework to specify algorithms building class hierarchies. Inform. Theor. Appl. 34, 521–548 (2000)

    Article  MATH  Google Scholar 

  19. Kent, R.: Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundam. Inform. 27, 169–181 (1996)

    MATH  Google Scholar 

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

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

    Article  MATH  Google Scholar 

  22. Liquiere, M., Sallantin, J.: Structural machine learning with Galois lattice and graphs. In: Proceedings of the 15th International Conference on Machine Learning, pp. 305–313 (1998)

  23. Mineau, G.W., Stumme, G., Wille, R.: Conceptual structures represented by conceptual graphs and formal concept analysis. In: Tepfenhart, W.M., Cyre, W. (eds.) Conceptual structures: Standards and Practices, vol. 1640, pp. 423–441 (1999)

  24. Pasquier, N., Bastide, Y., Taouil, T., Lakhal, L.: Efficient mining of association rules using closed itemset lattices. Inf. Syst. 24(1), 25–46 (1999)

    Article  Google Scholar 

  25. Rational Software Corporation: UML v 1.3, Notation Guide, version 1.3 edition (1999)

  26. Rayside, D., Campbell, G.T.: An aristotelian understanding of object-oriented programming. In: Doug Lea (ed.) Proceedings of OOPSLA’00, Minneapolis, MN, USA, pp. 337–353 (October 2000)

  27. Rumbaugh, J., Blaha, M., Premerlani, W., Eddy, F., Lorensen, W.: Object Oriented Modeling and Design. Prentice-Hall, Englewoods Cliff, NJ (1991)

    Google Scholar 

  28. Snelting, G., Tip, F.: Reengineering class hierarchies using concept analysis. In: Proceedings of ACM SIGPLAN/SIGSOFT Symposium on Foundations of Software Engineering, Orlando, FL, pp. 99–110(1998)

  29. Valtchev, P.: Building classes in object-based languages by automatic clustering. In: Hand, D., Kok, J., Berthold, M. (eds.) Proceedings of the 3rd International Symposium on Intelligent Data Analysis, vol. 1642, pp. 303–314 (1999)

  30. Valtchev, P., Grosser, D., Roume, C., Hacene, M.R.: Galicia: an open platform for lattices. In: de Moor, A., Ganter, B. (eds.) Using Conceptual Structures: Contributions to 11th Intl. Conference on Conceptual Structures (ICCS’03), pp. 241–254. Shaker, Aachen, Germany (2003)

    Google Scholar 

  31. Valtchev, P., Hacene, R.M., Huchard, M., Roume, C.: Extracting formal concepts out of relational data. In: SanJuan, E., Berry, A., Sigayret, A., Napoli, A. (eds.) Proceedings of the 4th Intl. Conference Journées de l’Informatique Messine (JIM’03): Knowledge Discovery and Discrete Mathematics, Metz (FR), 3–6 September, pp. 37–49. INRIA (2003)

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

    Article  MATH  Google Scholar 

  33. Vogt, F., Wille, R.: TOSCANA – a graphical tool for analyzing and exploring data. In: Tamassia, R., Tollis, I.G. (eds.) Graph Drawing, vol. 894, pp. 226–233 (1994)

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

    Google Scholar 

  35. Wille, R.: Conceptual structures of multicontexts. In: Eklund, P.W., Ellis, G., Mann, G. (eds.) Proceedings of the 4th ICCS 1996, Sidney (AU), vol. 1115, pp. 23–39 (1996)

  36. Yahia, A., Lakhal, L., Cicchetti, R., Bordat, J.P.: iO2 – An algorithmic method for building inheritance graphs in object database design. In: Proceedings of the 15th International Conference on Conceptual Modeling ER’96, vol. 1157, pp. 422–437 (1996)

Download references

Author information

Authors and Affiliations

  1. LIRMM, UMR 5506, CNRS et Université Montpellier 2, 161 rue Ada, 34392, Montpellier Cedex 5, France

    M. Huchard

  2. DIRO, Université de Montréal, CP 6128, Succ. Centre-Ville, Montréal, Québec, H3C 3J7, Canada

    M. Rouane Hacene, C. Roume & P. Valtchev

Authors
  1. M. Huchard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Rouane Hacene
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Roume
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Valtchev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Huchard.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huchard, M., Hacene, M.R., Roume, C. et al. Relational concept discovery in structured datasets. Ann Math Artif Intell 49, 39–76 (2007). https://doi.org/10.1007/s10472-007-9056-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-007-9056-3

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation