September 1, 1977
Additive Similarity Trees
Key Points
- This research aims to explore additive trees as a model for representing similarity data and to compare them with other methods.
- Developed a computer program, ADDTREE, to construct additive trees.
- Applied ADDTREE to several data sets to demonstrate its effectiveness.
- Compared results of additive trees with multidimensional scaling representations.
- Additive trees show empirical advantages over traditional spatial representations of proximity data.
- The comparison highlights the flexibility of additive trees compared to ultrametric trees.
- The findings indicate that tree representations can better capture the structure of dissimilarity data.
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.
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Authors
S
Shmuel Sattath
Hebrew University of Jerusalem
Amos Tversky
Hebrew College
Journals
Psychometrika
Actions
Institutions
Hebrew University of Jerusalem
References and Citations
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