Abstract
We study a new approach to regression analysis. We propose a new rule-based regression model using the theoretical framework of belief functions. For this purpose we use the recently proposed Evidential c-means (ECM) to derive rule-based models solely from data. ECM allocates, for each object, a mass of belief to any subsets of possible clusters, which allows to gain a deeper insight on the data while being robust with respect to outliers. The proposed rule-based models convey this added information as the examples illustrate.
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References
Shafer, G.: A mathematical theory of evidence. Princeton university press (1976)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its aplication to modeling and control. IEEE Transactions on Systems, Man and Cybernetics 15, 116–132 (1985)
Hartigan, J.A.: Clustering Algorithms. Wiley Interscience, New York (1974)
Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66, 191–234 (1994)
Masson, M.H., Denoeux, T.: ECM: An evidential version of the fuzzy c-means algorithm. Pattern Recognition 41, 1384–1397 (2008)
Tanaka, H., Uejima, S., Asai, K.: Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man and Cybernetics 12, 903–907 (1982)
Chang, Y.H.O., Ayyub, B.M.: Fuzzy regression methods - a comparative assessment. Fuzzy Sets and Systems 119, 187–203 (2001)
Ramdani, M., Mourot, G., Ragot, J.: A multi-modeling strategy based on belief function theory. In: 44th IEEE Conference on Decision and Control 2005 and 2005 European Control Conference, CDC-ECC 2005, pp. 3261–3266 (2005)
Petit-Renaud, S., Denoeux, T.: Nonparametric regression analysis of uncertain and imprecise data using belief functions. International Journal of Approximate Reasoning 35, 1–28 (2004)
Denoeux, T.: Function approximation in the framework of evidence theory: A connectionist approach. In: Proceedings of the 1997 International Conference on Neural Networks, Houston, USA (1997)
Smets, P.: The transferable belief model for quantified belief representation. In: Gabbay, D., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Kluwer, Dordrecht (1998)
Smets, P.: The combination of evidence in the transferable belief model. IEEE Trans. Pattern Anal. Mach. Intell. 12, 447–458 (1990)
Smets, P.: Decision making in the TBM: the necessity of the pignistic transformation. Int. J. Approx. Reasoning 38, 133–147 (2005)
Masson, M.H., Denux, T.: RECM: Relational evidential c-means algorithm. Pattern Recogn. Lett. 30, 1015–1026 (2009)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Quost, B., Masson, M.H., Denoeux, T.: Classifier fusion in the dempster-shafer framework using optimized t-norm based combination rules. International Journal of Approximate Reasoning 52, 353–374 (2011); Dependence Issues in Knowledge-Based Systems
Kallel, A., Hégarat-Mascle, S.L.: Combination of partially non-distinct beliefs: The cautious-adaptive rule. International Journal of Approximate Reasoning 50, 1000–1021 (2009); Special Section on Graphical Models and Information Retrieval
Klement, E., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)
Box, G.E.P., Jenkins, G.M.: Time Series Analysis, Forecasting, and Control. Holden-Day, San Francisco (1976)
Gustfson, D., Kessel, W.: Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of IEEE Conference on Decision and Control, CDC, San Diego, CA, USA, pp. 761–766 (1979)
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Almeida, R.J., Denoeux, T., Kaymak, U. (2012). Constructing Rule-Based Models Using the Belief Functions Framework. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_57
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DOI: https://doi.org/10.1007/978-3-642-31718-7_57
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