Abstract
In this paper, an innovative method for estimating mass functions using Kohonen’s Self Organizing Map is proposed. Our approach allows a smart mass belief assignment, not only for simple hypotheses, but also for disjunctions and conjunctions of hypotheses. This new method is of interest for solving estimation mass functions problems where a large quantity of multi-variate data is available. Indeed, the use of Kohonen map that allows to approximate the feature space dimension into a projected 2D space (so called map) simplifies the process of assigning mass functions. Experimentation on a benchmark database shows that our approach gives similar or better results than other methods presented in the literature so far, with an ability to handle large amount of data.
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References
Dempster, A.P.: Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals of Mathematical Statistics 38, 325–339 (1967)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, NJ (1976)
Smarandache, F., Dezert, J.: Advances and Applications of DSmT for Information Fusion (Collected works), vol. 1, 2 & 3. American Research Press, Rehoboth (2004-2009), http://www.gallup.unm.edu/~smarandache/DSmT.htm
Smets, P.: Belief functions: The Disjunctive Rule of Combination and the Generalized Bayesian Theorem. In: Yager, R.R., Liu, L. (eds.) Classic Works of the Dempster-Shafer Theory of Belief Functions. STUDFUZZ, vol. 219, pp. 633–664. Springer, Heidelberg (2008)
Zouhal, L.M., Denœux, T.: An Evidence-Theoretic K-NN Rule with Parameter Optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part C 28(2), 263–271 (1998)
Masson, M.H., Denœux, T.: ECM: An Evidential Version of the Fuzzy C-means Algorithm. Pattern Recogn. 41(4), 1384–1397 (2008)
Kohonen, T.: The Self-Organizing Map. Proceedings of the IEEE 78(9), 1464–1480 (1990)
Kraaijveld, M.A., Mao, J., Jain, A.K.: A Nonlinear Projection Method Based on Kohonen’s Topology Preserving Maps. IEEE Trans. Neural Networks 6(3), 548–559 (1995)
Chang, C.: An Information Theoretic-based Measure for Spectral Similarity and Discriminability. IEEE Trans. on Information Theory 46(5), 1927–1932 (2000)
Inglada, J., Mercier, G.: A New Statistical Similarity Measure for Change Detection in Multitemporal SAR Images and its Extension to Multiscale Change Analysis. IEEE Trans. on Geosci. Remote Sensing 45(5), 1432–1446 (2007)
Denœux, T., Masson, M.H.: EVCLUS: EVidential CLUSstering of Proximity Data. IEEE Trans. on Systems, Man, and Cybernetics, Part B 34(1), 95–109 (2004)
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Hammami, I., Dezert, J., Mercier, G., Hamouda, A. (2014). On the Estimation of Mass Functions Using Self Organizing Maps. In: Cuzzolin, F. (eds) Belief Functions: Theory and Applications. BELIEF 2014. Lecture Notes in Computer Science(), vol 8764. Springer, Cham. https://doi.org/10.1007/978-3-319-11191-9_30
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DOI: https://doi.org/10.1007/978-3-319-11191-9_30
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11190-2
Online ISBN: 978-3-319-11191-9
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