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
Bauer, M.: Approximations for efficient computation in the theory of evidence. Arttif. Intell. 61(2), 315–329 (1993)
Bosse, E., Jousselme, A.-L., Grenier, D.: A new distance between two bodies of evidence. Information Fusion 2, 91–101 (2001)
Cover, T.M., Hart, P.E.: Hart, Nearest neighbor pattern classification. IEEE Trans. Inform. Theory IT-13, 21–27 (1967)
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)
Elouedi, Z., Mellouli, K., Smets, P.: Belief Decision trees: Theoretical foundations. International Journal of Approximat Reasoning 28(2-3), 91–124 (2001)
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)
Fixen, D., Mahler, R.P.S.: The modified Dempster-Shafer approach to classification. IEEE Trans. Syst. Man Cybern. A 27(1), 96–104 (1997)
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)
Jain, A.K., Dubes, R.C.: Algorithms for clustering data. Prentice-Hall, Englewood cliffs (1988)
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)
Murphy, P.M., Aha, D.W.: Uci repository databases (1996), http://www.ics.uci.edu/mlearn
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)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Smets, Ph., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)
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)
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)
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)
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)
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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
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