, Volume 46, Issue 3, pp 351–352 | Cite as

Note on ultrametric hierarchical clustering algorithms

  • Vladimir Batagelj
Notes And Comments


Milligan presented the conditions that are required for a hierarchical clustering strategy to be monotonic, based on a formula by Lance and Williams. In the present paper, the statement of the conditions is improved and shown to provide necessary and sufficient conditions.

Key words

monotonic hierarchical clustering strategies 


  1. Lance, G. N. & Williams, W. T. A general theory of classificatory sorting strategies, 1. Hierarchical systems.The Computer Journal, 1967,9, 373–380.Google Scholar
  2. Milligan, G. W. Ultrametric hierarchical clustering algorithms.Psychometrika, 1979,44, 343–346.Google Scholar

Copyright information

© The Psychometric Society 1981

Authors and Affiliations

  • Vladimir Batagelj
    • 1
  1. 1.Department of MathematicsUniversity Edvard KardeljLjubljanaYugoslavia

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