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Enhancing MML Clustering Using Context Data with Climate Applications

  • Gerhard Visser
  • David L. Dowe
  • Petteri Uotila
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5866)

Abstract

In Minimum Message Length (MML) clustering (unsupervised classification, mixture modelling) the aim is to infer a set of classes that best explains the observed data items. There are cases where parts of the observed data do not need to be explained by the inferred classes but can be used to improve the inference and resulting predictions. Our main contribution is to provide a simple and flexible way of using such context data in MML clustering. This is done by replacing the traditional mixing proportion vector with a new context matrix. We show how our method can be used to give evidence regarding the presence of apparent long-term trends in climate-related atmospheric pressure records. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) solutions for our model have also been implemented to compare with the MML solution.

Keywords

Bayesian Information Criterion Code Length Minimum Description Length Context Data Class Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Cassano, J.J., Uotila, P., Lynch, A.: Changes in synoptic weather patterns in the polar regions in the twentieth and twenty-first centuries, part 1: Arctic. International Journal of Climatology 26(8), 1027–1049 (2006)CrossRefGoogle Scholar
  2. 2.
    Chaitin, G.J.: On the length of programs for computing finite binary sequences. Journal of the Association of Computing Machinery 13, 547–569 (1966)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Christainsen, B.: Atmospheric Circulation Regimes: Can Cluster Analysis Provide the Number? Climate Journal 20(10), 2229–2250 (2007)CrossRefGoogle Scholar
  4. 4.
    Comley, J.W., Dowe, D.L.: Minimum message length and generalized Bayesian nets with asymmetric languages. In: Grünwald, P., Pitt, M.A., Myung, I.J. (eds.) Advances in Minimum Description Length: Theory and Applications, pp. 265–294. MIT Press, Cambridge (2005)Google Scholar
  5. 5.
    Dowe, D.L.: Foreword re C. S. Wallace. Computer Journal 51(5), 523–560 (2008)CrossRefGoogle Scholar
  6. 6.
    Dowe, D.L., Gardner, S., Oppy, G.R.: Bayes not bust! Why simplicity is no problem for Bayesians. British J. Philosophy of Science, 709–754 (December 2007)Google Scholar
  7. 7.
    Edgoose, T., Allison, L.: MML Markov classification of sequential data. Statistics and Computing 9, 269–278 (1999)CrossRefGoogle Scholar
  8. 8.
    Edwards, R.T., Dowe, D.L.: Single factor analysis in MML mixture modeling. In: Wu, X., Kotagiri, R., Korb, K.B. (eds.) PAKDD 1998. LNCS (LNAI), vol. 1394, pp. 96–109. Springer, Heidelberg (1998)Google Scholar
  9. 9.
    Grunwald, P., Langford, J.: Suboptimal behavior of Bayes and MDL in classification under misspecification. Machine Learning 66(2-3), 119–149 (2007)CrossRefGoogle Scholar
  10. 10.
    Jebara, T.: Discriminative, Generative and Imitative learning. PhD thesis, MIT (2001)Google Scholar
  11. 11.
    Kohonen, T.: Self-Organizing Maps, vol. 30. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  12. 12.
    Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Problems of Information Transmission 1, 1–17 (1965)Google Scholar
  13. 13.
    Reusch, D.B., Alley, R.B.: Relative performance of Self-Organizing Maps and Principal Component Analysis in pattern extraction from synthetic climatological data. Polar Geography 29(3), 188–212 (2005)CrossRefGoogle Scholar
  14. 14.
    Rissanen, J.: Modeling by the shortest data description. Automatica 14, 465–471 (1978)zbMATHCrossRefGoogle Scholar
  15. 15.
    Solomonoff, R.J.: A formal theory of inductive inference. Information and Control 7, 1–22, 224–254 (1964)Google Scholar
  16. 16.
    Wallace, C.S.: Statistical and Inductive Inference by Minimum Message Length. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  17. 17.
    Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11, 185–194 (1968)zbMATHGoogle Scholar
  18. 18.
    Wallace, C.S., Dowe, D.L.: Intrinsic classification by MML - the Snob program. In: Proc. 7th Australian Joint Conf. on Artificial Intelligence, pp. 37–44. World Scientific, Singapore (1994)Google Scholar
  19. 19.
    Wallace, C.S., Dowe, D.L.: Minimum message length and Kolmogorov complexity. Computer Journal 42(4), 270–283 (1999)zbMATHCrossRefGoogle Scholar
  20. 20.
    Wallace, C.S., Dowe, D.L.: MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions. Statistics and Computing 10, 73–83 (2000)CrossRefGoogle Scholar
  21. 21.
    Wallace, C.S., Freeman, P.R.: Estimation and inference by compact coding. J. Royal Statistical Society B 49, 240–252 (1987)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gerhard Visser
    • 1
  • David L. Dowe
    • 1
  • Petteri Uotila
    • 1
  1. 1.Monash UniversityMelbourneAustralia

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