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

RAIRO - Operations Research (2010)

- Volume: 33, Issue: 3, page 339-365
- ISSN: 0399-0559

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topLerman, Israel-Cesar. "Comparing classification tree structures: a special case of comparing q-ary relations ." RAIRO - Operations Research 33.3 (2010): 339-365. <http://eudml.org/doc/197829>.

@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 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.
},

author = {Lerman, Israel-Cesar},

journal = {RAIRO - Operations Research},

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

language = {eng},

month = {3},

number = {3},

pages = {339-365},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/197829},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Lerman, Israel-Cesar

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

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 3

SP - 339

EP - 365

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 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.

LA - eng

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

UR - http://eudml.org/doc/197829

ER -

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