Classification using belief functions: Relationship between case-based and model-based approaches

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 36, Issue 6, 2006, Pages 1395-1405

  Denœux, Thierry ^a,b   Smets, Philippe ^c  

^a IEEE   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

^c UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Belief functions; Classification; Dempster Shafer theory; Evidence theory; Evidential reasoning; Pattern recognition; Supervised learning

Indexed keywords

DEMPSTER SHAFER THEORY; EVIDENCE THEORY; EVIDENTIAL REASONING; GENERAL BAYESIAN THEOREM (GBT); KERNEL RULE; PROBABILITY MODELS;

BAYESIAN NETWORKS; FORMAL LOGIC; FUNCTION EVALUATION; MATHEMATICAL MODELS; PATTERN RECOGNITION; PROBABILITY; SUPERVISED LEARNING;

UNCERTAIN SYSTEMS;

EID: 33947108026     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2006.877795     Document Type: Article

References (37)

1. J. Aitchison and I. R. Dunsmore, Statistical Prediction Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1975.
2. A. Appriou, "Probabilités et incertitude en fusion de données multi-senseurs," Revue Sci. Tech. Défense, vol. 1, no. 11, pp. 27-40, 1991.
3. _, "Uncertain data aggregation in classification and tracking processes," in Aggregation and Fusion of Imperfect Information, B. Bouchon-Meunier, Ed. Heidelberg, Germany: Physica-Verlag, 1998, pp. 231-260.
4. A. Bastière, "Methods for multisensor classification of airbone targets integrating evidence theory," Aerosp. Sci. Technol., vol. 2, no. 6, pp. 401-411, 1998.
5. S. Benferhat, A. Saffiotti, and P. Smets, "Belief functions and default reasoning," Artif. Intell., vol. 122, no. 1-2, pp. 1-69, 2000.
6. A.-S. Capelle, O. Colot, and C. Femandez-Maloigne, "Evidential segmentation scheme of multi-echo MR images for the detection of brain tumors using neighborhood information," Inf. Fusion, vol. 5, no. 3, pp. 203-216, 2004.
7. A. P. Dempster, "Upper and lower probabilities induced by a multivalued mapping," Ann. Math. Statist., vol. 38, no. 2, pp. 325-339, 1967.
8. T. Denœux, "A k-nearest neighbor classification rule based on Dempster-Shafer theory," IEEE Trans. Syst., Man, Cybern., vol. 25, no. 5, pp. 804-813, 1995.
9. _, "Analysis of evidence-theoretic decision rules for pattern classification," Pattern Recognit., vol. 30, no. 7, pp. 1095-1107, 1997.
10. _, "A neural network classier based on Dempster-Shafer theory," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 30, no. 2, pp. 131-150, Mar. 2000.
11. T. Denœux and L. M. Zouhal, "Handling possibilistic labels in pattern classification using evidential reasoning," Fuzzy Sets Syst., vol. 122, no. 3, pp. 47-62, 2001.
12. L. Devroye, L. Gyorfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition. New York: Springer-Verlag, 1996.
13. D. Dubois and H. Prade, "A set-theoretic view of belief functions: Logical operations and approximations by fuzzy sets," Int. J. Gen. Syst., vol. 12, no. 3, pp. 193-226, 1986.
14. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification. NewYork: Wiley, 2001.
15. K. Fukunaga, Introduction to Statistical Pattern Recognition. Boston, MA: Academic, 1990.
16. E. Hüllermeier, "Similarity-based inference as evidential reasoning," Int. J. Approx. Reasoning, vol. 26, no. 2, pp. 67-100, 2001.
17. E. Lefèvre, O. Colot, and P. Vannoorenberghe, "Belief function combination and conflict management," Inf. Fusion, vol. 3, no. 2, pp. 149-162, 2002.
18. N. K. Pal and S. Gosh, "Some classification algorithms integrating Dempster-Shafer theory of evidence with the rank nearest neighbor rule," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 31, no. 1, pp. 59-66, 2001.
19. S. Petit-Renaud and T. Denœux, "Nonparametric regression analysis of uncertain and imprecise data using belief functions," Int. J. Approx. Reasoning, vol. 35, no. 1, pp. 1-28, 2004.
20. B. D. Ripley, Pattern Recognition and Neural Networks. Cambridge, U.K.: Cambridge Univ. Press, 1996.
21. G. Shafer, A Mathematical Theory of Evidence. Princeton, N.J.: Princeton Univ. Press, 1976.
22. _, "Belief functions and parametric models," J. R. Statist. Soc. Ser. B, vol. 44, ho. 3, pp. 322-352, 1982. (with discussion).
23. H. Shen and K.-C. Chou, "Predicting protein subnuclear location with optimized evidence-theoretic K-nearest classier and pseudo amino acid composition," Biochem. Biophys. Res. Commun., vol. 337, no. 3, pp. 752-756, 2005.
24. _, "Using optimized evidence-theoretic K-nearest neighbor classier and pseudo-amino acid composition to predict membrane protein types," Biochem. Biophys. Res. Commun., vol. 334, no. 1, pp. 288-292, 2005.
25. P. Smets, "Un modèle mathématico-statistique simulant le processus du diagnostic médical," Ph.D. dissertation, Univ. Libre de Bruxelles, Brussels, Belgium, 1978.
26. _, "The combination of evidence in the transferable belief model," IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 5, pp. 447-458, May 1990.
27. _, "Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem," Int. J. Approx. Reasoning, vol. 9, no. 1, pp. 1-35, 1993.
28. _, "The normative representation of quantized beliefs by belief functions," Artif. Intell., vol. 92, no. 1-2, pp. 229-242, 1997.
29. _, "The transferable belief model for quantied belief representation," in Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. l, D. M. Gabbay and P. Smets, Eds. Dordrecht, The Netherlands: Kluwer, 1998, pp. 267-301.
30. _, "Decision making in the TBM: The necessity of the pignistic transformation," Int. J. Approx. Reasoning, vol. 38, no. 2, pp. 133-147, 2005.
31. P. Smets and R. Kennes, "The Transferable Belief Model," Artif. Intell., vol. 66, no. 2, pp. 191-243, 1994.
32. P. Vannoorenberghe and T. Denœux, "Likelihood-based versus distance-based evidential classier," in Proc. 10th IEEE Int. Conf. Fuzzy Syst., Dec. 2001, vol. 1, pp. 320-323.
33. B.-S. Yang and K. J. Kim, "Application of Dempster-Shafer theory in fault diagnosis of induction motors using vibration and current signals," Mech. Syst. Signal Process., vol. 20, no. 2, pp. 403-420, Feb. 2006.
34. N. M. Zaki, S. Deris, S. N. V. Arjunan, and R. M. Illias, "Assignment of protein sequence to functional family using neural network and Dempster-Shafer theory," J. Theoretics, vol. 5, no. 1, 2003.
35. W. Zhong, G. Altun, X. Tian, R. Harrison, P. C. Tai, and Y. Pan, "Parallel protein secondary structure prediction based on neural networks," in Proc. 26th Anna. Int. Conf. EMBC, 2004, pp. 2968-2971.
36. H. Zhu and O. Basir, "An adaptive fuzzy evidential nearest neighbor formulation for classifying remote sensing images," IEEE Trans. Geosci. Remote Sens., vol. 43, no. 8, pp. 1874-1888, Aug. 2005.
37. L. M. Zouhal and T. Denœux, "An evidence-theoretic k-NN. rule with parameter optimization," IEEE Trans. Syst., Man, Cybem. C, Appl. Rev., vol. 28, no. 2, pp. 263-271, May 1998.