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

Published online by Cambridge University Press:  15 August 2002

I. C. Lerman  and
F. Rouxel
I. C. Lerman
Affiliation:
Irisa - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France.
F. Rouxel
Affiliation:
Irisa - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France.
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Abstract

Comparing q-ary relations on a set $\cal O$ of elementary objects is one of the most fundamental problems ofclassification and combinatorial data analysis. In this paper the specific comparison task that involves classificationtree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One isdefined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches totree comparison are discussed in the context of a set theoretic representation of these relations. Formal andcombinatorial computing aspects of a construction method for a very general family of association coeficients betweenrelations are presented. The main purpose of this article is to specify the components of this construction, based on apermutational procedure, when the structures to be compared are classification trees.

Keywords

Classification treerelationsmathematical representationrandom permutational model.
Type
Research Article
Information
RAIRO - Operations Research , Volume 34 , Issue 3 , July 2000 , pp. 251 - 281
Copyright
© EDP Sciences, 2000

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