Abstract
An algorithm is developed for constructing a least-squares ultrametric tree representation of a possibly incomplete set of three-way one-mode dissimilarity data. The three-way distance among any three terminal nodes of an ultrametric tree is defined as the weight attached to the lowest common ancestor of the three nodes. A mathematical programming procedure is described for finding an ultrametric tree whose three-way distances approximate the corresponding observed three-way dissimilarities optimally in a least-squares sense. The algorithm is illustrated on some empirical data. In the final section, some of the advantages of the present approach are discussed and some possible extensions of the algorithm are mentioned.
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De Soete, G., Daws, J.T. (2000). Least-Squares Ultrametric Tree Representations of Three- Way One-Mode Proximity Data. In: Gaul, W., Opitz, O., Schader, M. (eds) Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58250-9_11
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DOI: https://doi.org/10.1007/978-3-642-58250-9_11
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