Additive similarity trees

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.

[1]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[2]  S. S. Yau,et al.  Distance matrix of a graph and its realizability , 1965 .

[3]  S. C. Johnson.  Hierarchical clustering schemes , 1967, Psychometrika.

[4]  L. Guttman.  A general nonmetric technique for finding the smallest coordinate space for a configuration of points , 1968 .

[5]  Teodor Kuennapas,et al.  Multidimensional Similarity of Letters , 1969, Perceptual and motor skills.

[6]  N. Henley.  A psychological study of the semantics of animal terms , 1969 .

[7]  James Turner,et al.  A Survey of Progress in Graph Theory in the Soviet Union , 1970 .

[8]  Amnon Rapoport,et al.  Structures in the subjective lexicon , 1971 .

[9]  P. Buneman.  The Recovery of Trees from Measures of Dissimilarity , 1971 .

[10]  E. Holman.  The relation between hierarchical and euclidean models for psychological distances , 1972 .

[11]  S. Hakimi,et al.  The distance matrix of a graph and its tree realization , 1972 .

[12]  Peter H. A. Sneath,et al.  Numerical Taxonomy: The Principles and Practice of Numerical Classification , 1973 .

[13]  R. Shepard.  Representation of structure in similarity data: Problems and prospects , 1974 .

[14]  P. Buneman.  A Note on the Metric Properties of Trees , 1974 .

[15]  A. Dobson.  Unrooted trees for numerical taxonomy , 1974, Journal of Applied Probability.

[16]  J. Carroll,et al.  Spatial, non-spatial and hybrid models for scaling , 1976 .

[17]  A. Tversky.  Features of Similarity , 1977 .