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Zbl 0948.05023
Lerman, Israël-César
Comparing classification tree structures: A special case of comparing $q$-ary relations. (English)
[J] RAIRO, Oper. Res. 33, No.3, 339-365 (1999). ISSN 0399-0559; ISSN 1290-3868/e

Summary: Comparing $q$-ary relations on a set ${\cal O}$ of elementary objects is one of the most fundamental problems of classification and combinatorial data analysis. In this paper the specific comparison task that involves classification tree structures (binary or not) is considered in this context. Two mathematical representations are 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 the context of a set theoretic representation of these relations. Formal and combinatorial computing aspects of a construction method for a very general family of association coefficients between relations are presented. The main purpose of this article is to specify the components of this construction, based on a permutational procedure, when the structures to be compared are classification trees.

MSC 2000:: *05C05 Trees
62H30 Statistical classification, etc.
90C27 Combinatorial programming

Keywords: classification tree; relations; mathematical representation; random permutational model

Cited in: Zbl 0955.05026

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