Equitable Conceptual Clustering Using OWA Operator

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10939)


We propose an equitable conceptual clustering approach based on multi-agent optimization, where each cluster is represented by an agent having its own satisfaction. The problem consists in finding the best cumulative satisfaction while emphasizing a fair compromise between all individual agents. The fairness goal is achieved using an equitable formulation of the Ordered Weighted Averages (OWA) operator. Experiments performed on UCI and ERP datasets show that our approach efficiently finds clusterings of consistently high quality.


  1. 1.
    Babaki, B., Guns, T., Nijssen, S.: Constrained clustering using column generation. In: Simonis, H. (ed.) CPAIOR 2014. LNCS, vol. 8451, pp. 438–454. Springer, Cham (2014). Scholar
  2. 2.
    Banerjee, A., Ghosh, J.: Scalable clustering algorithms with balancing constraints. Data Min. Knowl. Discov. 13(3), 365–395 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bouveret, S., Lemaître, M.: Computing leximin-optimal solutions in constraint networks. Artif. Intell. 173(2), 343–364 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chabert, M., Solnon, C.: Constraint programming for multi-criteria conceptual clustering. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 460–476. Springer, Cham (2017). Scholar
  5. 5.
    Chong, K.M.: An induction theorem for rearrangements. Candadian J. Math. 28, 154–160 (1976)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dao, T., Duong, K., Vrain, C.: Constrained clustering by constraint programming. Artif. Intell. 244, 70–94 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Dubois, D., Fortemps, P.: Computing improved optimal solutions to max-min flexible constraint satisfaction problems. EJOR 118, 95–126 (1999)CrossRefGoogle Scholar
  8. 8.
    Golden, B., Perny, P.: Infinite order Lorenz dominance for fair multiagent optimization. In: AAMAS, pp. 383–390 (2010)Google Scholar
  9. 9.
    Kostreva, M.M., Ogryczak, W., Wierzbicki, A.: Equitable aggregations and multiple criteria analysis. EJOR 158(2), 362–377 (2004)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Marshall, W., Olkin, I.: Inequalities: Theory of Majorization and its Applications. Academic Press, London (1979)zbMATHGoogle Scholar
  11. 11.
  12. 12.
    Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge (1989). Cambridge BookszbMATHGoogle Scholar
  13. 13.
    Mueller, M., Kramer, S.: Integer linear programming models for constrained clustering. In: Pfahringer, B., Holmes, G., Hoffmann, A. (eds.) DS 2010. LNCS (LNAI), vol. 6332, pp. 159–173. Springer, Heidelberg (2010). Scholar
  14. 14.
    Ogryczak, W., Sliwinski, T.: On solving linear programs with the ordered weighted averaging objective. EJOR 148(1), 80–91 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ouali, A., Loudni, S., Lebbah, Y., Boizumault, P., Zimmermann, A., Loukil, L.: Efficiently finding conceptual clustering models with integer linear programming. IJCAI 2016, 647–654 (2016)Google Scholar
  16. 16.
    Ouali, A., Zimmermann, A., Loudni, S., Lebbah, Y., Cremilleux, B., Boizumault, P., Loukil, L.: Integer linear programming for pattern set mining; with an application to tiling. In: Kim, J., Shim, K., Cao, L., Lee, J.-G., Lin, X., Moon, Y.-S. (eds.) PAKDD 2017. LNCS (LNAI), vol. 10235, pp. 286–299. Springer, Cham (2017). Scholar
  17. 17.
    Pensa, R.G., Robardet, C., Boulicaut, J.-F.: A bi-clustering framework for categorical data. In: Jorge, A.M., Torgo, L., Brazdil, P., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 643–650. Springer, Heidelberg (2005). Scholar
  18. 18.
    Perkowitz, M., Etzioni, O.: Adaptive web sites: conceptual cluster mining. In: IJCAI, vol. 99, pp. 264–269 (1999)Google Scholar
  19. 19.
    Sen, A., Foster, J.: On Economic Inequality. Clarendon Press, Oxford (1997)Google Scholar
  20. 20.
    Uno, T., Asai, T., Uchida, Y., Arimura, H.: An efficient algorithm for enumerating closed patterns in transaction databases. In: Suzuki, E., Arikawa, S. (eds.) DS 2004. LNCS (LNAI), vol. 3245, pp. 16–31. Springer, Heidelberg (2004). Scholar
  21. 21.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Yang, Y., Padmanabhan, B.: Segmenting customer transactions using a pattern-based clustering approach. In: ICDM, Vol. 2003, pp. 411–418 (2003)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lab. LITIO, University of Oran 1OranAlgeria
  2. 2.Normandie Univ, UNICAEN, ENSICAEN, CNRS, GREYCCaenFrance

Personalised recommendations