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Robust Cluster Analysis of Discrete Multivariate Observations

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Abstract

Cluster analysis of discrete multivariate observations containing outliers in a sample of a mixture of polynomial distributions is studied. A robust decision rule (stable to outliers) is designed in terms of analytically computed risk (probability of erroneous classification). A practical method of realization of the decision rule as a robust clustering procedure is developed and its effectiveness is determined both analytically and experimentally.

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REFERENCES

  1. Zhuk, E.E., Robust Cluster Analysis in the Presence of Anamolous Observations, Avtom.Telemekh., 1998, no. 9, pp. 72–87.

  2. Aivazyan, S.A., Bukhshtaber, V.M., Enyukov, I.S., et al., Prikladnaya statistika: klassifikatsiya i snizhenie razmernosti (Applied Statistics: Classification and Dimensional Reduction), Moscow: Finansy i Statistika, 1989.

    Google Scholar 

  3. Kharin, Yu.S., Robustness in Statistical Pattern Recognition, Dordrecht: Kluwer Academic, 1996.

    Google Scholar 

  4. Kendall, M. and Stuart, A., The Advanced Theory of Statistics, vol. 2: Inference and Relationship,, London: Charles Grifin, 1966. Translated under the title Statisticheskie vyvody i svyazi, Moscow: Nauka, 1973.

    Google Scholar 

  5. Brownlee, K.A., Statistical Theory and Methodology in Science and Engineering, New York: Wiley, 1960. Translated under the title Statisticheskaya teoriya i metodologiya v nauke i tekhnike, Moscow: Nauka, 1977.

    Google Scholar 

  6. Huber, P.J., Robust Statistics, New York: Wiley, 1981. Translated under the title Robastnost' v statistike, Moscow: Mir, 1984.

    Google Scholar 

  7. Kullback, S., Information Theory and Statistics, New York: Wiley, 1959.

    Google Scholar 

  8. Borovkov, A.A., Matematicheskaya statistika (Mathematical Statistics), Moscow: Nauka, 1984.

    Google Scholar 

  9. Hampel, F.R., Roncetti, E.M., Rausseew, P.J., and Stahel, W.A., Robust Statistics.The Approach Based on Influence Functions, New York: Wiley, 1986. Translated under the title Robastnost' v statistike: podkhod na osnove funktsii vliyaniya, Moscow: Mir, 1989.

    Google Scholar 

  10. Anderson, T.W., An Introduction to Multivariate Statistical Analysis, New York: Wiley, 1984. Translated under the title Vvedenie v mnogomernyi statisticheskii analiz, Moscow: Fizmatgiz, 1963.

    Google Scholar 

  11. Cramer, H., Mathematical Methods of Statistics, Princeton: Princeton Univ. Press, 1937. Translated under the title Matematicheskie metody statistiki, Moscow: Mir, 1975.

    Google Scholar 

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Authors and Affiliations

  1. Belarussian State University, Minsk, Belarus

    E. E. Zhuk

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  1. E. E. Zhuk
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Zhuk, E.E. Robust Cluster Analysis of Discrete Multivariate Observations. Automation and Remote Control 62, 114–123 (2001). https://doi.org/10.1023/A:1002888102969

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