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On the Bounds on Optimal Bayes Error in the Task of Multiple Data Sources

  • Conference paper
Image Processing and Communications Challenges 4

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 184))

Summary

The paper considers the problem of pattern recognition when we have multiple data sources. We assume that for each data source there are estimated parameters of statistical distributions. The model of classification is primarily based on the Bayes rule and secondarily on the notion of interval-valued fuzzy sets. The set of possible class-conditional probability density functions is represented by an interval-valued fuzzy set. We consider the case where the uncertainty concerns the mean of Gaussian pdf. In the paper the bound on the optimal Bayess error is presented for a full probabilistic information.

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References

  1. Okuda, T., Tanaka, H., Asai, K.: A formulation of fuzzy decision problems with fuzzy information using probability measures of fuzzy events. Information and Control 38, 135–147 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. Goguen, J.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18(1), 145–174 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  4. Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Information Science 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mitchell, H.B.: Pattern recognition using type-II fuzzy sets. Information Science 170, 409–418 (2005)

    Article  Google Scholar 

  8. Zeng, J., Liu, Y.-Q.: Type-2 fuzzy markov random fields and their application to handwritten chinese character recognition. IEEE Transactions on Fuzzy Systems 16(3), 747–760 (2008)

    Article  Google Scholar 

  9. Jia, Z., Lei, X., Zhi-Qiang, L.: Type-2 fuzzy Gaussian mixture models. Pattern Recognition 41, 3636–3643 (2008)

    Article  MATH  Google Scholar 

  10. Antos, A., Devroye, L., Gyorfi, L.: Lower bounds for Bayes error estimation. IEEE Trans. Pattern Analysis and Machine Intelligence 21, 643–645 (1999)

    Article  Google Scholar 

  11. Avi-Itzhak, H., Diep, T.: Arbitrarily tight upper and lower bounds on the bayesian probability of error. IEEE Trans. Pattern Analysis and Machine Intelligence 18, 89–91 (1996)

    Article  Google Scholar 

  12. Kulkarni, A.: On the mean accuracy of hierarchical classifiers. IEEE Transactions on Computers 27, 771–776 (1978)

    Article  MATH  Google Scholar 

  13. Kurzyński, M.: On the multistage Bayes classifier. Pattern Recognition 21, 355–365 (1988)

    Article  MATH  Google Scholar 

  14. Kittler, J.: Combining classifiers: A theoretical framework. Pattern Analysis and Applications 1, 18–27 (1998)

    Article  Google Scholar 

  15. Woźniak, M.: Experiments on linear combiners. In: Pietka, E., Kawa, J. (eds.) Information Tech. in Biomedicine. ASC, vol. 47, pp. 445–452. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Burduk, R.: Classification error in Bayes multistage recognition task with fuzzy observations. Pattern Analysis and Applications 13(1), 85–91 (2010)

    Article  MathSciNet  Google Scholar 

  17. Pardo, L., Menendez, M.L.: Some bounds on probability of error in fuzzy discrimination problems. European Journal of Operational Research 53, 362–370 (1991)

    Article  MATH  Google Scholar 

  18. Pardo, J.A., Taneja, I.J.: On the probability of error in fuzzy discrimination Problems. Kybernetes 21(6), 43–52 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kuncheva, L.I.: Combining pattern classifier: Methods and Algorithms. John Wiley, New York (2004)

    Book  MATH  Google Scholar 

  20. Zeng, J., Xie, L., Liu, Y.-Q.: Type-2 fuzzy Gaussian mixture models. Pattern Recognition 41, 3636–3643 (2008)

    Article  MATH  Google Scholar 

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Correspondence to Robert Burduk .

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Burduk, R. (2013). On the Bounds on Optimal Bayes Error in the Task of Multiple Data Sources. In: Choraś, R. (eds) Image Processing and Communications Challenges 4. Advances in Intelligent Systems and Computing, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32384-3_25

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  • DOI: https://doi.org/10.1007/978-3-642-32384-3_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32383-6

  • Online ISBN: 978-3-642-32384-3

  • eBook Packages: EngineeringEngineering (R0)

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