Abstract
Similarity data can be represented by additive trees. In this model, objects are represented by the external nodes of a tree, and the dissimilarity between objects is the length of the path joining them. The additive tree is less restrictive than the ultrametric tree, commonly known as the hierarchical clustering scheme. The two representations are characterized and compared. A computer program, ADDTREE, for the construction of additive trees is described and applied to several sets of data. A comparison of these results to the results of multidimensional scaling illustrates some empirical and theoretical advantages of tree representations over spatial representations of proximity data.
Keywords
Ultrametric spaceMultidimensional scalingSimilarity (geometry)Tree (set theory)MathematicsHierarchical clusteringCluster analysisScalingPath (computing)SimilitudeData miningTheoretical computer scienceComputer scienceStatisticsArtificial intelligenceMetric spaceCombinatoricsDiscrete mathematicsImage (mathematics)
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Publication Info
- Year
- 1977
- Type
- article
- Volume
- 42
- Issue
- 3
- Pages
- 319-345
- Citations
- 598
- Access
- Closed
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Cite This
Shmuel Sattath,
Amos Tversky
(1977).
Additive Similarity Trees.
Psychometrika
, 42
(3)
, 319-345.
https://doi.org/10.1007/bf02293654
Identifiers
- DOI
- 10.1007/bf02293654