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

RAIRO - Operations Research (2010)

- Volume: 34, Issue: 3, page 251-281
- ISSN: 0399-0559

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topLerman, I. C., and Rouxel, F.. "Comparing classification tree structures: A special case of comparing q-ary relations II." RAIRO - Operations Research 34.3 (2010): 251-281. <http://eudml.org/doc/197789>.

@article{Lerman2010,

abstract = {
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 coeficients 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.
},

author = {Lerman, I. C., Rouxel, F.},

journal = {RAIRO - Operations Research},

keywords = {Classification tree; relations; mathematical representation; random permutational model.; -ary relations; classification tree structures},

language = {eng},

month = {3},

number = {3},

pages = {251-281},

publisher = {EDP Sciences},

title = {Comparing classification tree structures: A special case of comparing q-ary relations II},

url = {http://eudml.org/doc/197789},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Lerman, I. C.

AU - Rouxel, F.

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

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 3

SP - 251

EP - 281

AB -
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 coeficients 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.

LA - eng

KW - Classification tree; relations; mathematical representation; random permutational model.; -ary relations; classification tree structures

UR - http://eudml.org/doc/197789

ER -

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