Advertisement

On a New Evidential C-Means Algorithm with Instance-Level Constraints

  • Jiarui XieEmail author
  • Violaine Antoine
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11940)

Abstract

Clustering is an unsupervised task whose performances can be highly improved with background knowledge. As a consequence, several semi-supervised clustering approaches have proposed to integrate prior information in the form of constraints, generally at the instance-level. Amongst them, evidential semi-supervised clustering algorithms, such as CECM or SECM algorithm, rely on the theoretical foundation of belief function which extends the probabilistic theory and allows us to express many types of uncertainty about the assignment of an object to a cluster. In this framework, no evidential clustering algorithm has ever mixed different types of instance-level constraints. We propose here to combine pairwise constraints and labeled data constraints in order to better retrieve information from the background knowledge. The new algorithm, called LPECM, shows good performances on synthetic and real data sets.

Keywords

Labeled data constraints Pairwise constraints Instance-level constraints Belief function Evidential clustering Semi-supervised clustering 

References

  1. 1.
    Antoine, V., Quost, B., Masson, M.H., Denœux, T.: CEVCLUS: evidential clustering with instance-level constraints for relational data. Soft Comput. - Fusion Found. Methodol. Appl. 18(7), 1321–1335 (2014)Google Scholar
  2. 2.
    Antoine, V., Gravouil, K., Labroche, N.: On evidential clustering with partial supervision. In: Destercke, S., Denoeux, T., Cuzzolin, F., Martin, A. (eds.) BELIEF 2018. LNCS (LNAI), vol. 11069, pp. 14–21. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-99383-6_3CrossRefGoogle Scholar
  3. 3.
    Antoine, V., Labroche, N., Vu, V.V.: Evidential seed-based semi-supervised clustering. In: International Symposium on Soft Computing & Intelligent Systems, Kitakyushu, Japan (2014)Google Scholar
  4. 4.
    Antoine, V., Quost, B., Masson, M.H., Denœux, T.: CECM: constrained evidential C-means algorithm. Comput. Stat. Data Anal. 56(4), 894–914 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy C-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)CrossRefGoogle Scholar
  6. 6.
    Bilenko, M., Basu, S., Mooney, R.: Integrating constraints and metric learning in semi-supervised clustering. In: Proceedings of the Twenty-First International Conference on Machine Learning. ACM New York, NY, USA (2004)Google Scholar
  7. 7.
    Coleman, T.F., Li, Y.: A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables. SIAM J. Optim. 6(4), 1040–1058 (1996)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Denœux, T.: Evidential clustering of large dissimilarity data. Knowl.-Based Syst. 106(C), 179–195 (2016)CrossRefGoogle Scholar
  9. 9.
    Dua, D., Graff, C.: UCI machine learning repository (2017). http://archive.ics.uci.edu/ml
  10. 10.
    Grira, N., Crucianu, M., Boujemaa, N.: Active semi-supervised fuzzy clustering. Pattern Recogn. 41(5), 1834–1844 (2008)CrossRefGoogle Scholar
  11. 11.
    Gustafson, D.E., Kessel, W.C.: Fuzzy clustering with a fuzzy covariance matrix. In: IEEE Conference on Decision & Control Including the Symposium on Adaptive Processes, New Orleans, LA (2007) Google Scholar
  12. 12.
    Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)CrossRefGoogle Scholar
  13. 13.
    Li, F., Li, S., Denoeux, T.: k-CEVCLUS: constrained evidential clustering of large dissimilarity data. Knowl.-Based Syst. 142, 29–44 (2018)CrossRefGoogle Scholar
  14. 14.
    Masson, M.H., Denœux, T.: ECM: an evidential version of the fuzzy C-means algorithm. Pattern Recogn. 41(4), 1384–1397 (2008)CrossRefGoogle Scholar
  15. 15.
    Shafer, G.: A Mathematical Theory of Evidence, vol. 42. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  16. 16.
    Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–234 (1994)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Vu, V.V., Do, H.Q., Dang, V.T., Do, N.T.: An efficient density-based clustering with side information and active learning: a case study for facial expression recognition task. Intell. Data Anal. 23(1), 227–240 (2019)CrossRefGoogle Scholar
  18. 18.
    Wagstaff, K., Cardie, C., Rogers, S., Schrœdl, S.: Constrained k-means clustering with background knowledge. In: Proceedings of the Eighteenth International Conference on Machine Learning (ICML), Williamstown, MA, USA, vol. 1, pp. 577–584 (2001)Google Scholar
  19. 19.
    Zhang, H., Lu, J.: Semi-supervised fuzzy clustering: a kernel-based approach. Knowl.-Based Syst. 22(6), 477–481 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Clermont Auvergne University, UMR 6158 CNRS, LIMOSClermont-FerrandFrance
  2. 2.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinPeople’s Republic of China

Personalised recommendations