Loevinger's measures of rule quality for assessing cluster stability
DeweyProbabilités et mathématiques appliquées
SujetCluster stability; Monte Carlo test; Cluster isolation and cluster cohesion; Loevinger’s measure; Number of clusters of a partition
Journal issueComputational Statistics & Data Analysis
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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.
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