L. Hubert, and P. Arabie. Journal of Classification, 2 (1):
193--218(1985)
Abstract
The problem of comparing two different partitions of a finite set
of objects reappears continually in the clustering literature. We
begin by reviewing a well-known measure of partition correspondence
often attributed to Rand (1971), discuss the issue of correcting
this index for chance, and note that a recent normalization strategy
developed by Morey and Agresti (1984) and adopted by others (e.g.,
Miligan and Cooper 1985) is based on an incorrect assumption. Then,
the general problem of comparing partitions is approached indirectly
by assessing the congruence of two proximity matrices using a simple
cross-product measure. They are generated from corresponding partitions
using various scoring rules. Special cases derivable include traditionally
familiar statistics and/or ones tailored to weight certain object
pairs differentially. Finally, we propose a measure based on the
comparison of object triples having the advantage of a probabilistic
interpretation in addition to being corrected for chance (i.e., assuming
a constant value under a reasonable null hypothesis) and bounded
between ±1. ER -
%0 Journal Article
%1 HubAra85
%A Hubert, Lawrence
%A Arabie, Phipps
%D 1985
%J Journal of Classification
%K cluster_evaluation
%N 1
%P 193--218
%T Comparing partitions
%U http://dx.doi.org/10.1007/BF01908075
%V 2
%X The problem of comparing two different partitions of a finite set
of objects reappears continually in the clustering literature. We
begin by reviewing a well-known measure of partition correspondence
often attributed to Rand (1971), discuss the issue of correcting
this index for chance, and note that a recent normalization strategy
developed by Morey and Agresti (1984) and adopted by others (e.g.,
Miligan and Cooper 1985) is based on an incorrect assumption. Then,
the general problem of comparing partitions is approached indirectly
by assessing the congruence of two proximity matrices using a simple
cross-product measure. They are generated from corresponding partitions
using various scoring rules. Special cases derivable include traditionally
familiar statistics and/or ones tailored to weight certain object
pairs differentially. Finally, we propose a measure based on the
comparison of object triples having the advantage of a probabilistic
interpretation in addition to being corrected for chance (i.e., assuming
a constant value under a reasonable null hypothesis) and bounded
between ±1. ER -
@article{HubAra85,
abstract = {The problem of comparing two different partitions of a finite set
of objects reappears continually in the clustering literature. We
begin by reviewing a well-known measure of partition correspondence
often attributed to Rand (1971), discuss the issue of correcting
this index for chance, and note that a recent normalization strategy
developed by Morey and Agresti (1984) and adopted by others (e.g.,
Miligan and Cooper 1985) is based on an incorrect assumption. Then,
the general problem of comparing partitions is approached indirectly
by assessing the congruence of two proximity matrices using a simple
cross-product measure. They are generated from corresponding partitions
using various scoring rules. Special cases derivable include traditionally
familiar statistics and/or ones tailored to weight certain object
pairs differentially. Finally, we propose a measure based on the
comparison of object triples having the advantage of a probabilistic
interpretation in addition to being corrected for chance (i.e., assuming
a constant value under a reasonable null hypothesis) and bounded
between ±1. ER -},
added-at = {2009-02-28T21:01:39.000+0100},
author = {Hubert, Lawrence and Arabie, Phipps},
biburl = {https://www.bibsonomy.org/bibtex/2348396ace6cc4de62cb9569a7147c8c0/tfalk},
description = {SpringerLink - Zeitschriftenbeitrag},
interhash = {c9272c8f9d5aff7ebe43325b5b36ba39},
intrahash = {348396ace6cc4de62cb9569a7147c8c0},
journal = {Journal of Classification},
keywords = {cluster_evaluation},
number = 1,
pages = {193--218},
timestamp = {2009-02-28T21:01:41.000+0100},
title = {Comparing partitions},
url = {http://dx.doi.org/10.1007/BF01908075},
volume = 2,
year = 1985
}