##
**Hierarchical clustering schemes.**
*(English)*
Zbl 1367.62191

Summary: 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”.

### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62P15 | Applications of statistics to psychology |

91C15 | One- and multidimensional scaling in the social and behavioral sciences |

Full Text:
DOI

### References:

[1] | Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–27. · Zbl 0123.36803 |

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

[3] | 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. |

[4] | Shepard, R. N. Analysis of proximities: Multidimensional scaling with an unknown distance function. I.Psychometrika, 1962a,27, 125–140. · Zbl 0129.12103 |

[5] | Shepard, R. N. Analysis of proximities: Multidimensional scaling with an unknown distance function. II.Psychometrika, 1962b,27, 219–246. · Zbl 0129.12103 |

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

[7] | Sokal, R. R. and Sneath, P. H. A.Principles of Numerical Taxonomy. San Francisco: W. H. Freeman, 1963. · Zbl 0285.92001 |

[8] | SĂ¸rensen, 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. |

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

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.