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Comparing classification tree structures:a special case of comparing q-ary relations

Published online by Cambridge University Press:  15 August 2002

Israel-Cesar Lerman
Israel-Cesar Lerman*
Affiliation:
Irisa, Université de Rennes 1, Campus de Beaulieu, Avenue du General Leclerc, 35042 Rennes Cedex, France.
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Abstract

Comparing q-ary relations on a set ${\cal O}$ ofelementary objects is one of the most fundamental problems ofclassification and combinatorial data analysis. In this paper thespecific comparison task that involvesclassification tree structures (binary or not) is considered in thiscontext. Two mathematical representationsare proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation.The most classical approaches to tree comparison are discussed in thecontext of a set theoretic representation of these relations. Formalandcombinatorial computing aspects of a construction method for a verygeneralfamily of association coefficients between relations are presented. The main purpose of this article is to specify the componentsof this construction, based on a permutational procedure, when thestructuresto be compared are classification trees.

Keywords

Classification treerelationsmathematical representationrandom permutational model.
Type
Research Article
Information
RAIRO - Operations Research , Volume 33 , Issue 3 , July 1999 , pp. 339 - 365
Copyright
© EDP Sciences, 1999

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