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Maximum Likelihood Estimation and Optimal Coordinates

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Advances in Systems Science (ICSS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 539))

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Abstract

We show that the MLE (maximum likelihood estimation) in the class of Gaussian densities can be understood as the search for the best coordinate system which “optimally” underlines the internal structure of the data. This allows in particular to the search for the optimal coordinate system when the origin is fixed in a given point.

P. Spurek—The paper was supported by the National Centre of Science (Poland) Grant No. 2013/09/N/ST6/01178.

J. Tabor— The paper was supported by the National Centre of Science (Poland) Grant No. 2014/13/B/ST6/01792.

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References

  1. Banfield, J.D., Raftery, A.E.: Model-based gaussian and non-gaussian clustering. Biometrics 49(3), 803–821 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bartlett, M.S.: An inverse matrix adjustment arising in discriminant analysis. Ann. Math. Stat. 22(1), 107–111 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  3. Borg, I., Groenen, P.: Modern multidimensional scaling: Theory and applications. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  4. Van den Bos, A.: Parameter Estimation for Scientists and Engineers. Wiley Online Library, New York (2007)

    MATH  Google Scholar 

  5. Celeux, G., Govaert, G.: Gaussian parsimonious clustering models. Pattern Recogn. 28(5), 781–793 (1995)

    Article  Google Scholar 

  6. Cover, T., Thomas, J., Wiley, J., et al.: Elements of Information Theory. Wiley Online Library, New York (1991)

    Book  Google Scholar 

  7. Grigorieff, R.: A note on von neumanns trace inequality. Math. Nachr. 151, 327–328 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  8. Han, J., Kamber, M., Pei, J.: Data Mining: Concepts and Techniques. Morgan Kaufmann, San Francisco (2011)

    MATH  Google Scholar 

  9. Krishnaiah, P.: Handbook of Statistics. North-Holland, New York (1988)

    Google Scholar 

  10. Kullback, S.: Information Theory and Statistics. Dover Publications, New York (1997)

    MATH  Google Scholar 

  11. Lehmann, E., Casella, G.: Theory of Point Estimation. Springer, New York (1998)

    MATH  Google Scholar 

  12. De Maesschalck, R., Jouan-Rimbaud, D., Massart, D.: The mahalanobis distance. Chemometr. Intell. Lab. Syst. 50(1), 1–18 (2000)

    Article  Google Scholar 

  13. Mahalanobis, P.C.: On the generalised distance in statistics. Proc. Nat. Inst. Sci. 2, 49–55 (1936)

    MATH  Google Scholar 

  14. Mirsky, L.: A trace inequality of john von neumann. Monatshefte für mathematik 79(4), 303–306 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ng, S., Krishnan, T., McLachlan, G.: The em algorithm. In: Gentle, J.E., Härdle, W.K., Mori, Y. (eds.) Handbook of Computational Statistics Concepts and Methods. Springer Handbooks of Computational Statistics, pp. 139–172. Springer, Heidelberg (2004)

    Google Scholar 

  16. Nielsen, F., Nock, R.: Sided and symmetrized bregman centroids. IEEE Trans. Inf. Theory 55(6), 2882–2904 (2009)

    Article  MathSciNet  Google Scholar 

  17. Raykov, T., Marcoulides, G.: An Introduction to Applied Multivariate Analysis. Routledge, London (2008)

    MATH  Google Scholar 

  18. Rencher, A.: Methods of Multivariate Analysis. Wiley Online Library, New York (1995)

    MATH  Google Scholar 

  19. Theobald, C.: An inequality with application to multivariate analysis. Biometrika 62(2), 461–466 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  20. Timm, N.: Applied Multivariate Analysis. Springer, New York (2002)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

    P. Spurek & J. Tabor

Authors
  1. P. Spurek
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  2. J. Tabor
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Correspondence to P. Spurek .

Editor information

Editors and Affiliations

  1. Wroclaw University of Science and Technology, Wroclaw, Poland

    Jerzy Świątek

  2. Wroclaw University of Science and Technology, Wroclaw, Poland

    Jakub M. Tomczak

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Spurek, P., Tabor, J. (2017). Maximum Likelihood Estimation and Optimal Coordinates. In: Świątek, J., Tomczak, J. (eds) Advances in Systems Science. ICSS 2016. Advances in Intelligent Systems and Computing, vol 539. Springer, Cham. https://doi.org/10.1007/978-3-319-48944-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-48944-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48943-8

  • Online ISBN: 978-3-319-48944-5

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