Tree-tree matrices and other combinatorial problems from taxonomy
type: Item
instance of: scholarly article
title: Tree-tree matrices and other combinatorial problems from taxonomy
zbMATH Open document ID: 0847.05024
author: Michiel Hazewinkel
published in: European Journal of Combinatorics
publication date: 1996-07-03T00:00:00Z
review text: Much of the literature on mathematical taxonomy and clustering has focused on the question of `abstracting' from a given dissimilarity a suitable (classification) tree. A central question is ``given a metric on a space \(X\), which is the metric corresponding to a hierarchical classification scheme, which best approximates the given one?'' It may be that trees are not really as appropriate for classification and information-finding purposes as their dominance in the literature implies. It may be that trees are a relic of the use of hard copy: they are just about the only classification scheme which can be more or less decently printed. A bipartite graph \(A\) between two sets \(D\) and \(T\) may be used to transfer (classification) information from one of the two sets to the other. \(A\) defines, via Hamming distance, metrics on both \(T\) and \(D\). It is shown that if both spaces are trivial \(A\) comes from an Hadamard matrix or a BIBD.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 871015
zbMATH Keywords: classification trees
zbMATH Keywords: mathematical taxonomy
zbMATH Keywords: metrics
zbMATH Keywords: Hadamard matrix
zbMATH Keywords: BIBD
reviewed by: Jennifer Seberry
MaRDI profile type: Publication
full work available at URL: eujc.1996.0017
OpenAlex ID: W2144023495
DOI: 10.1006/EUJC.1996.0017
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description: scientific article; zbMATH DE number 871015