Advertisement

Theory of a Probabilistic-Dependence Measure of Dissimilarity Among Multiple Clusters

  • Kazunori Iwata
  • Akira Hayashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4132)

Abstract

We introduce novel dissimilarity to properly measure dissimilarity among multiple clusters when each cluster is characterized by a probability distribution. This measure of dissimilarity is called redundancy-based dissimilarity among probability distributions. From aspects of source coding, a statistical hypothesis test and a connection with Ward’s method, we shed light on the theoretical reasons that the redundancy-based dissimilarity among probability distributions is a reasonable measure of dissimilarity among clusters.

Keywords

IEEE Transaction Information Source Machine Intelligence Dissimilarity Measure Multiple Cluster 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. John Wiley & Sons, New York (2001)MATHGoogle Scholar
  2. 2.
    Xu, R., Wunsch-II, D.C.: Survey of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)CrossRefGoogle Scholar
  3. 3.
    Gokcay, E., Principle, J.C.: Information theoretic clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(2), 158–171 (2002)CrossRefGoogle Scholar
  4. 4.
    Maulik, U., Bandyopadhyay, S.: Performance evaluation of some clustering algorithms and validity indices. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(12), 1650–1654 (2002)CrossRefGoogle Scholar
  5. 5.
    Webb, A.R.: Statistical Pattern Recognition, 2nd edn. John Wiley & Sons, New York (2002)MATHCrossRefGoogle Scholar
  6. 6.
    Yeung, D., Wang, X.: Improving performance of similarity-based clustering by feature weight learning. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(4), 556–561 (2002)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Fred, A.L., Leitão, J.M.: A new cluster isolation criterion based on dissimilarity increments. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(8), 944–958 (2003)CrossRefGoogle Scholar
  8. 8.
    Yang, M.S., Wu, K.L.: A similarity-based robust clustering method. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(4), 434–448 (2004)CrossRefGoogle Scholar
  9. 9.
    Tipping, M.E.: Deriving cluster analytic distance functions from gaussian mixture model. In: Proceedings of the 9th International Conference on Artificial Neural Networks, Edinburgh, UK, vol. 2, pp. 815–820. IEE (1999)Google Scholar
  10. 10.
    Prieto, M.S., Allen, A.R.: A similarity metric for edge images. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(10), 1265–1273 (2003)CrossRefGoogle Scholar
  11. 11.
    Wei, J.: Markov edit distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(3), 311–321 (2004)CrossRefGoogle Scholar
  12. 12.
    Srivastava, A., Joshi, S.H., Mio, W., Liu, X.: Statistical shape analysis: Clustering, learning, and testing. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(4), 590–602 (2005)CrossRefGoogle Scholar
  13. 13.
    Österreicher, F.: On a class of perimeter-type distances of probability distributions. Cybernetics 32(4), 389–393 (1996)MATHGoogle Scholar
  14. 14.
    Topsøe, F.: Some inequalities for information divergence and related measures of discrimination. IEEE Transactions on Information Theory 46(4), 1602–1609 (2000)CrossRefGoogle Scholar
  15. 15.
    Endres, D.M., Schindelin, J.E.: A new metric for probability distributions. IEEE Transactions on Information Theory 49(7), 1858–1860 (2003)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Sanov, I.N.: On the probability of large deviations of random variables. Selected Translations in Mathematical Statistics and Probability 1, 213–244 (1961)MATHMathSciNetGoogle Scholar
  17. 17.
    Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Applications of Mathematics, vol. 38. Springer, New York (1998)MATHGoogle Scholar
  18. 18.
    Han, T.S., Kobayashi, K.: Mathematics of Information and Coding. Translations of Mathematical Monographs, vol. 203. American Mathematical Society, Providence (2002)MATHGoogle Scholar
  19. 19.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 1st edn. Wiley series in telecommunications. John Wiley & Sons, Inc., New York (1991)MATHCrossRefGoogle Scholar
  20. 20.
    Ward, J.H.: Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association 58(301), 236–244 (1963)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Ward, J.H., Hook, M.E.: Application of an hierarchical grouping procedure to a problem of grouping profiles. Educational Psychological Measurement 23(1), 69–82 (1963)CrossRefGoogle Scholar
  22. 22.
    Gärtner, J.: On large deviations from the invariant measure. Theory of Probability and Its Applications 22, 24–39 (1977)MATHCrossRefGoogle Scholar
  23. 23.
    Ellis, R.S.: Large deviations for a general class of random vectors. The Annals of Probability 12(5), 1–12 (1984)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kazunori Iwata
    • 1
  • Akira Hayashi
    • 1
  1. 1.Faculty of Information SciencesHiroshima City UniversityHiroshimaJapan

Personalised recommendations