Refinement Properties in Agglomerative Hierarchical Clustering

  • Sadaaki Miyamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5861)


Refinement properties that means each cluster of a method is included in another cluster of another method in agglomerative clustering which was proposed by Miyamoto are further studied. Although we have simple conditions so that a method generates refinements of clusters of the single linkage method, whether or not generalizations hold when the single linkage is not used is unknown. Here three conditions for refinement properties for the single linkage are shown, while three counterexamples are shown for the average linkage and the complete linkage, which show the theory of refinements is far from trivial and future works are needed.


Agglomerative clustering refinement single linkage complete linkage average linkage 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderberg, M.R.: Cluster Analysis for Applications. Academic Press, New York (1973)zbMATHGoogle Scholar
  2. 2.
    Everitt, B.S.: Cluster Analysis, 3rd edn. Arnold, London (1993)Google Scholar
  3. 3.
    Miyamoto, S.: Fuzzy Sets in Information Retrieval and Cluster Analysis. Kluwer, Dordrecht (1990)zbMATHGoogle Scholar
  4. 4.
    Miyamoto, S.: Introduction to Cluster Analysis: Theory and Applications of Fuzzy Clustering, Morikita-Shuppan, Tokyo (1990) (in Japanese)Google Scholar
  5. 5.
    Miyamoto, S.: Data Clustering Algorithms for Information Systems. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 13–24. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sadaaki Miyamoto
    • 1
  1. 1.Department of Risk Engineering Faculty of Systems and Information EngineeringUniversity of TsukubaJapan

Personalised recommendations