Least squares algorithms for constructing constrained ultrametric and additive tree representations of symmetric proximity data

Geert De Soete, J. Douglas Carroll, Wayne S. DeSarbo

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

A mathematical programming algorithm is developed for fitting ultrametric or additive trees to proximity data where external constraints are imposed on the topology of the tree. The two procedures minimize a least squares loss function. The method is illustrated on both synthetic and real data. A constrained ultrametric tree analysis was performed on similarities between 32 subjects based on preferences for ten odors, while a constrained additive tree analysis was carried out on some proximity data between kinship terms. Finally, some extensions of the methodology to other tree fitting procedures are mentioned.

Original languageEnglish (US)
Pages (from-to)155-173
Number of pages19
JournalJournal of Classification
Volume4
Issue number2
DOIs
StatePublished - Sep 1 1987

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Psychology (miscellaneous)
  • Statistics, Probability and Uncertainty
  • Library and Information Sciences

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