A Unifying Framework for Classification Procedures Based on Cluster Aggregation by Choquet Integral

  • Luigi Troiano
Part of the Communications in Computer and Information Science book series (CCIS, volume 297)


A unifying framework for classification procedures which makes use of clustering and utility aggregation by (a variant of) Choquet integral is introduced. The model is presented as a general framework which looks at classification as an aggregation of information induced by clusters, so that the decision to which class unlabelled points should belong is taken by considering the whole space. Classification procedures k-nearest neighbor (k-NN) and classification trees (CT) are reformulated within the proposed framework. In addition, the model can be used to define a new classification procedures. An example is provided and compared to the others when applied to two UCI datasets.


Classification k-NN nearest neighbors decision tree classification tree Choquet integral 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beliakov, G., James, S.: Using choquet integrals for knn approximation and classification. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2008. IEEE World Congress on Computational Intelligence, pp. 1311–1317 (June 2008)Google Scholar
  2. 2.
    Choquet, G.: Theory of capacities. In: Annales de l’institut Fourier, vol. 5, pp. 131–295 (1954)Google Scholar
  3. 3.
    Hüllermeier, E.: Cho-k-nn: a method for combining interacting pieces of evidence in case-based learning. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence, IJCAI 2005, pp. 3–8. Morgan Kaufmann Publishers Inc., San Francisco (2005)Google Scholar
  4. 4.
    Liu, H.-C., Jheng, Y.-D., Chen, G.-S., Jeng, B.-C.: A new classification algorithm combining choquet integral and logistic regression. In: 2008 International Conference on Machine Learning and Cybernetics, vol. 6, pp. 3072–3077 (June 2008)Google Scholar
  5. 5.
    Mendez-Vazquez, A., Gader, P., Keller, J.M., Chamberlin, K.: Minimum classification error training for choquet integrals with applications to landmine detection. IEEE Transactions on Fuzzy Systems 16(1), 225–238 (2008)CrossRefGoogle Scholar
  6. 6.
    Takahagi, E.: Multiple-Output Choquet Integral Models and Their Applications in Classification Methods. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds.) Nonlinear Mathematics for Uncertainty and its Applications. AISC, vol. 100, pp. 93–100. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Wu, K., Wang, Z., Heng, P.-A., Leung, K.-S.: Using generalized choquet integral in projection pursuit based classification. In: Joint 9th IFSA World Congress and 20th NAFIPS International Conference, vol. 1, pp. 506–511 (2001)Google Scholar
  8. 8.
    Xu, K., Wang, Z., Heng, P.-A., Leung, K.-S.: Classification by nonlinear integral projections. IEEE Transactions on Fuzzy Systems 11(2), 187–201 (2003)CrossRefGoogle Scholar
  9. 9.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man and Cybernetics 18(1), 183–190 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Yang, R., Wang, Z., Heng, P.-A., Leung, K.-S.: Classification of heterogeneous fuzzy data by choquet integral with fuzzy-valued integrand. IEEE Transactions on Fuzzy Systems 15(5), 931–942 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Luigi Troiano
    • 1
  1. 1.Department of Engineering RCOSTUniversity of SannioBeneventoItaly

Personalised recommendations