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Using Dempster-Shafer Theory in MCF Systems to Reject Samples

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Book cover Multiple Classifier Systems (MCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3541))

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Abstract

In this paper the Dempster-Shafer theory of evidence is utilised in multiple classifier systems to define rejection criteria for samples presented for classification. The DS theory offers the possibility to derive a measure of contradiction between the classifier decisions to be fused. Moreover, assigning positive belief mass to the universal hypothesis Θ in the basic probability assignments produced by the classifiers, allows to quantify the belief in their correctness. Both criteria have been evaluated by numerical simulations on two different benchmark data sets. The results are compared to standard static classifier combination schemes and basic classifiers. It is shown that DS classifier fusion can boost the combined classifier accuracy to 100% on the set of accepted data points (~ 70%). This behaviour could be of interest in applications with high costs for a miss, e.g. in medical screening tests.

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References

  1. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)

    Google Scholar 

  2. Dubois, D., Prade, H.: Combination of information in the framework of possibility theory. In: Abidi, M.A., Gonzalez, R.C. (eds.) Data Fusion in Robotics and Machine Intelligence, pp. 481–505. Academic Press, London (1992)

    Google Scholar 

  3. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  4. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kuncheva, L.I., Bezdek, J.C., Duin, R.P.W.: Decision templates for multiple classifier fusion: An experimental comparison. Pattern Recognition 34, 299–314 (2001)

    Article  MATH  Google Scholar 

  6. Bloch, I.: Information combination operators for data fusion: A comparative review with classification. IEEE Transactions on Systems, Man and Cybernetics, Part A 26, 52–67 (1996)

    Article  Google Scholar 

  7. Dempster, A.P.: A generalization of Bayesian inference. Journal of the Royal Statistical Society 30, 205–247 (1968)

    MathSciNet  Google Scholar 

  8. Shafer, G.: A Mathematical Theory of Evidence. University Press, Princeton (1976)

    MATH  Google Scholar 

  9. Shafer, G.: Dempster-Shafer Theory (2002), http://www.glennshafer.com/assets/downloads/article48.pdf

  10. Grzymala-Busse, J.W.: Managing Uncertainty in Expert Systems. Kluwer Academic Publishers, Boston (1991)

    MATH  Google Scholar 

  11. Pomykalski, J.J., Truszkowski, W.F., Brown, D.E.: Expert systems. In: Webster, J. (ed.) Wiley Encyclopedia of Electronic and Electrical Engineering (1999)

    Google Scholar 

  12. Rogova, G.: Combining the results of several neural network classifiers. Neural Networks 7, 777–781 (1994)

    Article  Google Scholar 

  13. Xu, L., Krzyzak, A., Suen, C.Y.: Methods of combining multiple classifiers and their applications to handwriting recognition. IEEE Transactions on Systems, Man, and Cybernetics 22, 418–435 (1992)

    Article  Google Scholar 

  14. Denoeux, T.: A Neural Network Classifier Based on Dempster-Shafer Theory. IEEE Transactions on Systems, Man and Cybernetics, Part A 30, 131–150 (2000)

    Article  Google Scholar 

  15. Milisavljevic, N., Bloch, I.: Sensor fusion in anti-personnel mine detection using a two-level belief function model. IEEE Transactions on Systems, Man and Cybernetics, Part C 33, 269–283 (2003)

    Article  Google Scholar 

  16. Smets, P.: Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem. International Journal of Approximate Reasoning 9, 1–35 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zadeh, L.A.: Book review: A mathematical theory of evidence. AI Magazine 5, 81–83 (1984)

    Google Scholar 

  18. Heinsohn, J., Socher-Ambrosius, R.: Wissensverarbeitung. Eine Einführung. Spektrum Akademischer Verlag (1999)

    Google Scholar 

  19. Smets, P.: The nature of the unnormalized beliefs encountered in the transferable belief model. In: Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence, pp. 292–297. Morgan Kaufmann, San Mateo (1992)

    Google Scholar 

  20. Mandler, E., Schürmann, J.: Combining the classification results of independent classifiers based on the Dempster/Shafer theory of evidence. Pattern Recognition and Artificial Intelligence, 381–393 (1988)

    Google Scholar 

  21. Al-Ani, A., Deriche, M.: A new technique for combining multiple classifiers using the Dempster-Shafer theory of evidence. Journal of Artificial Intelligence Research 17, 333–361 (2002)

    MATH  MathSciNet  Google Scholar 

  22. Le Hegarat-Mascle, S., Richard, D., Ottle, C.: Multi-scale data fusion using Dempster-Shafer evidence theory. Integrated Computer-Aided Engineering 10, 9–22 (2003)

    Google Scholar 

  23. Fay, R., Kaufmann, U., Schwenker, F., Palm, G.: Learning Object Recognition in a NeuroBotic System. In: Groß, H.M., Debes, K., Böhme, H.J. (eds.) 3rd Workshop on SelfOrganization of AdaptiVE Behavior SOAVE 2004, Fortschritt-Berichte VDI, Reihe, VDI, vol. 743(10), pp. 198–209 (2004)

    Google Scholar 

  24. Gonzales, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Addison-Wesley, Reading (1992)

    Google Scholar 

  25. Smith, A.R.: Color gamut transform pairs. In: Proceedings of the 5th Annual Conference on Computer Graphics and Interactive Techniques, vol. 12, pp. 12–19 (1978)

    Google Scholar 

  26. Schwenker, F., Kestler, H.A., Palm, G.: Three learning phases for radial-basis-function networks. Neural Networks 14, 439–458 (2001)

    Article  Google Scholar 

  27. Thiel, C.: Multiple Classifier Fusion Incorporating Certainty Factors. Master’s thesis, University of Ulm, Germany (2004)

    Google Scholar 

  28. Michie, D., Spiegelhalter, D.J., Taylor, C.C. (eds.): Machine Learning, Neural and Statistical Classification. Ellis Horwood, New York (1994)

    MATH  Google Scholar 

  29. Karhuhnen, K.: Zur Spektraltheorie stochastischer Prozesse. Annales Academiae Scientiarum Fennicae 34 (1946)

    Google Scholar 

  30. Loève, M.M.: Probability Theory. Van Nostrand, Princeton (1955)

    Google Scholar 

  31. Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, New York (1990)

    MATH  Google Scholar 

  32. Shannon, C.: A mathematical theory of communication. Bell System Technical Journal 27, 379–423 (1948)

    MATH  MathSciNet  Google Scholar 

  33. Schürmann, J.: Pattern Classification, a unified view of statistical and neural approaches. John Wiley & Sons, Chichester (1996)

    Google Scholar 

  34. Kuncheva, L.I.: Using degree of consensus in two-level fuzzy pattern recognition. European Journal of Operational Research 80, 365–370 (1995)

    Article  Google Scholar 

  35. Dietrich, C., Palm, G., Schwenker, F.: Decision Templates for the Classification of Time Series. International Journal of Information Fusion 4 (2003)

    Google Scholar 

  36. Huang, Y.S., Suen, C.Y.: A method of combining multiple experts for the recognition of unconstrained handwritten numerals. IEEE Transactions on Pattern Analysis and Machine Intelligence 17, 90–94 (1995)

    Article  Google Scholar 

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Thiel, C., Schwenker, F., Palm, G. (2005). Using Dempster-Shafer Theory in MCF Systems to Reject Samples. In: Oza, N.C., Polikar, R., Kittler, J., Roli, F. (eds) Multiple Classifier Systems. MCS 2005. Lecture Notes in Computer Science, vol 3541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494683_12

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  • DOI: https://doi.org/10.1007/11494683_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26306-7

  • Online ISBN: 978-3-540-31578-0

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