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Hierarchical clustering schemes


Techniques for partitioning objects into optimally homogeneous groups on the basis of empirical measures of similarity among those objects have received increasing attention in several different fields. This paper develops a useful correspondence between any hierarchical system of such clusters, and a particular type of distance measure. The correspondence gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data. In an explicitly defined sense, one method forms clusters that are optimally “connected,” while the other forms clusters that are optimally “compact.”

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  • Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–27.

    Google Scholar 

  • McQuitty, L. L. Hierarchical linkage analysis for the isolation of types.Educational and Psychological Measurement, 1960,20, 55–67.

    Google Scholar 

  • Miller, G. A. and Nicely, P. E. An analysis of perceptual confusions among some English consonants.Journal of the Acoustical Society of America, 1955,27, 338–352.

    Google Scholar 

  • Shepard, R. N. Analysis of proximities: Multidimensional scaling with an unknown distance function. I.Psychometrika, 1962a,27, 125–140.

    Google Scholar 

  • Shepard, R. N. Analysis of proximities: Multidimensional scaling with an unknown distance function. II.Psychometrika, 1962b,27, 219–246.

    Google Scholar 

  • Sneath, P. H. A. The application of computers to taxonomy.Journal of General Microbiology, 1957,17, 201–226.

    Google Scholar 

  • Sokal, R. R. and Sneath, P. H. A.Principles of Numerical Taxonomy. San Francisco: W. H. Freeman, 1963.

    Google Scholar 

  • Sørensen, T. A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons.Biologiske Skrifter, 1948,5 (4), 1–34.

    Google Scholar 

  • Ward, J. H., Jr. Hierarchical grouping to optimize an objective function.Journal of the American Statistical Association, 1963,58, 236–244.

    Google Scholar 

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I am indebted to R. N. Shepard and J. D. Carroll for many stimulating discussions about this work, and for aid in preparing this paper.

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Johnson, S.C. Hierarchical clustering schemes. Psychometrika 32, 241–254 (1967).

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  • Public Policy
  • Hierarchical Cluster
  • Distance Measure
  • Statistical Theory
  • Homogeneous Group