Abstract
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.”
Keywords
Hierarchical clusteringCluster analysisMathematicsHomogeneousMonotonic functionInvariant (physics)Measure (data warehouse)Similarity (geometry)Cluster (spacecraft)Type (biology)Single-linkage clusteringBasis (linear algebra)Computer sciencePattern recognition (psychology)Data miningArtificial intelligenceFuzzy clusteringStatisticsCURE data clustering algorithmCombinatorics
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Publication Info
- Year
- 1967
- Type
- article
- Volume
- 32
- Issue
- 3
- Pages
- 241-254
- Citations
- 4785
- Access
- Closed
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Cite This
S. C. Johnson
(1967).
Hierarchical Clustering Schemes.
Psychometrika
, 32
(3)
, 241-254.
https://doi.org/10.1007/bf02289588
Identifiers
- DOI
- 10.1007/bf02289588