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Loevinger's measures of rule quality for assessing cluster stability

Bertrand, Patrice; Bel Mufti, Ghazi (2006), Loevinger's measures of rule quality for assessing cluster stability, Computational Statistics & Data Analysis, 50, 4, p. 992-1015. http://dx.doi.org/10.1016/j.csda.2004.10.012

Type
Article accepté pour publication ou publié
Date
2006
Journal name
Computational Statistics & Data Analysis
Volume
50
Number
4
Publisher
Elsevier
Pages
992-1015
Publication identifier
http://dx.doi.org/10.1016/j.csda.2004.10.012
Metadata
Show full item record
Author(s)
Bertrand, Patrice

Bel Mufti, Ghazi
Abstract (EN)
A method is developed for measuring clustering stability under the removal of a few objects from aset of objects to be partitioned. Measures of stability of an individual cluster are defined as Loevinger’smeasures of rule quality. The stability of an individual cluster can be interpreted as a weighted meanof the inherent stabilities in the isolation and cohesion, respectively, of the examined cluster. Thedesign of the method also enables us to measure the stability of a partition, that can be viewed as aweighted mean of the stability measures of all clusters in the partition. As a consequence, an approachis derived for determining the optimal number of clusters of a partition. Furthermore, using a MonteCarlo test, a significance probability is computed in order to assess how likely any stability measure is,under a null model that specifies the absence of cluster stability. In order to illustrate the potential ofthe method, stability measures that were obtained by using the batch K-Means algorithm on artificialdata sets and on Iris Data are presented.
Subjects / Keywords
Cluster stability; Monte Carlo test; Cluster isolation and cluster cohesion; Loevinger’s measure; Number of clusters of a partition

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