Abstract
A new classifier using neighborhood information in the framework of the Dempster-Shafer theory of evidence has recently been introduced. This approach consists in considering each neighbor of a pattern to be classified as an item of evidence supporting certain hypotheses concerning the class membership of that pattern. In this paper, an adaptive version of this method is proposed, in which the parameters used to define the basic probability assignments are learnt from the data by minimizing the mean squared error between the classifier outputs and target values. Based on the evidence-theoretic concepts of degree of conflict and ignorance, new reject rules are introduced. Several sets of artificial and real-world data are used for comparison with the voting and distanceweighted classifiers.
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References
T. M. Cover and P. E. Hart, “Nearest neighbor pattern classification”, IEEE Trans. Inform. Theory, vol. IT-13(1), 1967,pp. 21–27.
T. Denoeux, “Application of evidence theory to k-NN pattern classification”. In E. S. Gelsema and L-N Kanal (Editors), Pattern Recognition in Practice IV, Elsevier, Amsterdam, 1994, pp. 13–24.
T. Denoeux, “A k-nearest neighbor classification rule based on Dempster-Shafer theory”, IEEE Trans. Syst. Man. Cybern., vol. SMC-25(5), 1995, pp. 804–813.
B. V. Dasarathy, “Nosing around the neighborhood: A new system structure and classification rule for recognition in partially exposed environments”, IEEE Trans. Pattern Anal. Machine. Intell, vol. PAMI-2(1), 1980, pp. 67–71.
B. Dubuisson and M. Masson, “A statistical decision rule with incomplete knowledge about classes”, Pattern Recognition, vol. 26(1), 1993, pp. 155–165.
S. A. Dudani, “The distance-weighted k-nearest neighbor rule”, IEEE Trans. Syst. Man. Cybern., vol. SMC-6(4), 1976, pp. 325–327.
J. H. Friedman, “Regularized discriminant analysis”, J. Am. Statist. Ass., vol. 84, 1989, pp. 165–175.
M. E. Hellman, “The k-nearest neighbor classification rule with a reject option”, IEEE Trans. Syst. Man. Cybern., vol. SMC-6(3), 1970, pp. 155–165.
A. Jousselin and B. Dubuisson, “A link between k-nearest neighbor rules and knowledge based systems by sequence analysis”, Pattern Recognition Letters, vol. 6, 1987, pp. 287–295.
P. M. Murphy and D. W. Aha, UCI Reposition of machine learning databases [Machine-readable data repository], Irvine, CA, 1994.
G. Parthasarathy and B. N. Chatterji, “A class of new k-NN methods for low sample problems”, IEEE Trans. Syst. Man. Cybern., vol. SMC-6(4), 1990, pp. 715–718.
G. Shafer, A mathematical theory of evidence, Princeton N.J, Princeton University Press, 1976.
P. Smets, “The combination of evidence in the transferable belief model”, IEEE Trans. Pattern Anal. Machine. Intell. vol. PAMI-12(5), 1990, pp. 447–458.
P. Smets and R. Kennes, “The transferable belief model”, Artificial Intelligence vol. AI-66, 1994, pp. 191–234.
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© 1995 Springer-Verlag Berlin Heidelberg
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Zouhal, L.M., Denœux, T. (1995). An adaptive k-NN rule based on Dempster-Shafer theory. In: Hlaváč, V., Šára, R. (eds) Computer Analysis of Images and Patterns. CAIP 1995. Lecture Notes in Computer Science, vol 970. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60268-2_311
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DOI: https://doi.org/10.1007/3-540-60268-2_311
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