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Clustering Approach Using Belief Function Theory

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Artificial Intelligence: Methodology, Systems, and Applications (AIMSA 2006)

Abstract

Clustering techniques are considered as efficient tools for partitioning data sets in order to get homogeneous clusters of objects. However, the reality is connected to uncertainty by nature, and these standard algorithms of clustering do not deal with this uncertainty pervaded in their parameters. In this paper we develop a clustering method in an uncertain context based on the K-modes method and the belief function theory. This so-called belief K-modes method (BKM) provides a new clustering technique handling uncertainty in the attribute values of objects in both the clusters’ construction task and the classification one.

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References

  1. Bauer, M.: Approximations for efficient computation in the theory of evidence. Arttif. Intell. 61(2), 315–329 (1993)

    Article  Google Scholar 

  2. Bosse, E., Jousselme, A.-L., Grenier, D.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)

    Article  Google Scholar 

  3. Cover, T.M., Hart, P.E.: Hart, Nearest neighbor pattern classification. IEEE Trans. Inform. Theory IT-13, 21–27 (1967)

    Article  Google Scholar 

  4. Denoeux, T.: A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Transactions on Systems, Man and Cybernetics 25(5), 804–813 (1995)

    Article  Google Scholar 

  5. Elouedi, Z., Mellouli, K., Smets, P.: Belief Decision trees: Theoretical foundations. International Journal of Approximat Reasoning 28(2-3), 91–124 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Elouedi, Z., Mellouli, K., Smets, Ph.: Assessing sensor reliability for multisensor data fusion within the transferable belief model. IEEE Trans. Syst. Man Cybern. B Cybern. 34(1), 782–787 (2004)

    Article  Google Scholar 

  7. Fixen, D., Mahler, R.P.S.: The modified Dempster-Shafer approach to classification. IEEE Trans. Syst. Man Cybern. A 27(1), 96–104 (1997)

    Google Scholar 

  8. Huang, Z.: Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Mining Knowl. Discov. 2(2), 283–304 (1998)

    Article  Google Scholar 

  9. Jain, A.K., Dubes, R.C.: Algorithms for clustering data. Prentice-Hall, Englewood cliffs (1988)

    MATH  Google Scholar 

  10. MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proc. of the Fifth Berkeley Symposium on Math. Stat. and Prob., vol. 1, pp. 281–296 (1967)

    Google Scholar 

  11. Murphy, P.M., Aha, D.W.: Uci repository databases (1996), http://www.ics.uci.edu/mlearn

  12. Quinlan, J.R.: Learning efficient classification and their application to chess end games. In: Michalski, R.S., Carbonell, J.G., Michell, T.M. (eds.) Machine Learning: An artificial intelligence approach, pp. 463–482. Morgan Kaufmann, San Francisco (1983)

    Google Scholar 

  13. Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  14. Smets, Ph., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Rumelhart, D.E., McClelland, J.L. (eds.) Parallel Distributed Processing. MIT Press, Cambridge (1986)

    Google Scholar 

  16. Smets, Ph.: The transferable belief model for quantified belief representation. In: Gabbay, D.M., Smets, P. (eds.) Handbook of defeasible reasoning and uncertainty management systems, vol. 1, pp. 267–301 (1998b)

    Google Scholar 

  17. Tessem, B.: Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - an empirical study. Int. J. Approx. Reason. 17(2-3), 217 (1997)

    Article  Google Scholar 

  18. Zouhal, L.M., Denoeux, T.: An evidence-theory k-NN rule with parameter optimization. IEEE Trans. Syst. Man Cybern. C 28(2), 263–271 (1998)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Ben Hariz, S., Elouedi, Z., Mellouli, K. (2006). Clustering Approach Using Belief Function Theory. In: Euzenat, J., Domingue, J. (eds) Artificial Intelligence: Methodology, Systems, and Applications. AIMSA 2006. Lecture Notes in Computer Science(), vol 4183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861461_18

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  • DOI: https://doi.org/10.1007/11861461_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40930-4

  • Online ISBN: 978-3-540-40931-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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