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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
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