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Selecting External Validation Measures for K-means Clustering

  • Junjie Wu
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

Cluster validity is a long standing challenge in the clustering literature. While many evaluation measures have been developed for cluster validity, these measures often provide inconsistent information about the clustering performance, and the best suitable measures to use remain unclear in practice. Our study in this chapter fills this crucial void by giving an organized study of sixteen external validation measures for K-means clustering. Specifically, we first propose a filtering criterion based on the uniform effect of K-means, and apply it for the identification of defective measures.

Keywords

Cluster Result Cluster Performance Normalization Scheme Cluster Validation External Measure 
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.

References

  1. Ben-Hur, A., Guyon, I.: Detecting stable clusters using principal component analysis. Methods Mol. Biol. 224 (2003), 159–182 (2003) Google Scholar
  2. Brun, M., Sima, C., Hua, J., Lowey, J., Carroll, B., Suh, E., Dougherty, E.: Model-based evaluation of clustering validation measures. Pattern Recognit. 40 , 807–824 (2007) zbMATHCrossRefGoogle Scholar
  3. Childs, A., Balakrishnan, N.: Some approximations to the multivariate hypergeometric distribution with applications to hypothesis testing. Comput. Stat. Data Anal. 35 (2), 137–154 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  4. Cover, T., Thomas, J.: Elements of Information Theory, 2nd edn. Wiley-Interscience, New York (2006)zbMATHGoogle Scholar
  5. Dhillon, I., Mallela, S., Modha, D.: Information-theoretic co-clustering. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 89–98 (2003)Google Scholar
  6. van Dongen, S.: Performance criteria for graph clustering and markov cluster experiments. Technical report, Amsterdam, The Netherlands (2000)Google Scholar
  7. Fowlkes, E., Mallows, C.: A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc 78 , 553–569 (1983) zbMATHCrossRefGoogle Scholar
  8. Goodman, L., Kruskal, W.: Measures of association for cross classification. J. Am. Stat. Assoc 49 , 732–764 (1954) zbMATHGoogle Scholar
  9. Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Cluster validity methods: Part i. SIGMOD Rec. 31 (2), 40–45 (2002) CrossRefGoogle Scholar
  10. Hubert, L.: Nominal scale response agreement as a generalized correlation. Br. J. Math. Stat. Psychol. 30 , 98–103 (1977) MathSciNetzbMATHCrossRefGoogle Scholar
  11. Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2 , 193–218 (1985) CrossRefGoogle Scholar
  12. Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1988)zbMATHGoogle Scholar
  13. Kendall, M.: Rank Correlation Methods. Hafner Publishing Company, New York (1955)zbMATHGoogle Scholar
  14. Larsen, B., Aone, C.: Fast and effective text mining using linear-time document clustering. In: Proceedings of the 5th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 16–22 (1999)Google Scholar
  15. MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)Google Scholar
  16. Meila, M.: Comparing clusterings by the variation of information. In: Proceedings of the 16th Annual Conference on Computational Learning Theory, pp. 173–187 (2003)Google Scholar
  17. Meila, M.: Comparing clusterings–an axiomatic view. In: Proceedings of the 22nd International Conference on Machine learning, pp. 577–584 (2005)Google Scholar
  18. Mirkin, B.: Mathematical Classification and Clustering. Kluwer Academic Press, Dordrecht (1996)zbMATHCrossRefGoogle Scholar
  19. Rand, W.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66 , 846–850 (1971) CrossRefGoogle Scholar
  20. Rijsbergen, C.: Information Retrieval, 2nd edn. Butterworths, London (1979)Google Scholar
  21. Steinbach, M., Karypis, G., Kumar, V.: A comparison of document clustering techniques. In: Proceedings of the KDD Workshop on Text Mining (2000)Google Scholar
  22. Strehl, A., Ghosh, J., Mooney, R.: Impact of similarity measures on web-page clustering. In: Proceedings of the AAAI Workshop on AI for Web Search (2000)Google Scholar
  23. Wu, J., Xiong, H., Chen, J.: Adapting the right measures for k-means clustering. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 877–886. New York, NY, USA (2009)Google Scholar
  24. Zhao, Y., Karypis, G.: Criterion functions for document clustering: Experiments and analysis. Mach. Learn. 55 (3), 311–331 (2004) zbMATHCrossRefGoogle Scholar
  25. Zhong, S., Ghosh, J.: Generative model-based document clustering: a comparative study. Knowl. Inf. Syst. 8 (3), 374–384 (2005) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Junjie Wu
    • 1
  1. 1.Department of Information Systems, School of Economics and ManagementBeihang UniversityBeijingChina

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