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Minkowski Generalizations of Ward’s Method in Hierarchical Clustering

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  • Alan Lee
  • Bobby Willcox

Abstract

In this paper, we consider several generalizations of the popular Ward’s method for agglomerative hierarchical clustering. Our work was motivated by clustering software, such as the R function hclust, which accepts a distance matrix as input and applies Ward’s definition of inter-cluster distance to produce a clustering. The standard version of Ward’s method uses squared Euclidean distance to form the distance matrix. We explore the effect on the clustering of using other definitions of distance, such as the Minkowski distance. Copyright Classification Society of North America 2014

Suggested Citation

  • Alan Lee & Bobby Willcox, 2014. "Minkowski Generalizations of Ward’s Method in Hierarchical Clustering," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 194-218, July.
    • Handle: RePEc:spr:jclass:v:31:y:2014:i:2:p:194-218
    DOI: 10.1007/s00357-014-9157-8
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. Zhenmin Chen & John Ness, 1996. "Space-conserving agglomerative algorithms," Journal of Classification, Springer;The Classification Society, vol. 13(1), pages 157-168, March.
    3. Meila, Marina, 2007. "Comparing clusterings--an information based distance," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 873-895, May.
    4. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
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