Quotation Rusch, Thomas, Hornik, Kurt, Mair, Patrick. 2018. Assessing and quantifying clusteredness: The OPTICS Cordillera. Journal of Computational and Graphical Statistics, 27 (1), 220-233.




This article provides a framework for assessing and quantifying “clusteredness” of a data representation. Clusteredness is a global univariate property defined as a layout diverging from equidistance of points to the closest neighboring point set. The OPTICS algorithm encodes the global clusteredness as a pair of clusteredness-representative distances and an algorithmic ordering. We use this to construct an index for quantification of clusteredness, coined the OPTICS Cordillera, as the norm of subsequent differences over the pair. We provide lower and upper bounds and a normalization for the index. We show the index captures important aspects of clusteredness such as cluster compactness, cluster separation, and number of clusters simultaneously. The index can be used as a goodness-of-clusteredness statistic, as a function over a grid or to compare different representations. For illustration, we apply our suggestion to dimensionality reduced 2D representations of Californian counties with respect to 48 climate change related variables. Online supplementary material is available (including an R package, the data and additional mathematical details).


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Journal of Computational and Graphical Statistics
Citation Index SCI
WU-Journal-Rating new FIN-A, VW-C
Language English
Title Assessing and quantifying clusteredness: The OPTICS Cordillera
Volume 27
Number 1
Year 2018
Page from 220
Page to 233
Reviewed? Y
URL https://www.tandfonline.com/doi/full/10.1080/10618600.2017.1349664
DOI http://dx.doi.org/10.1080/10618600.2017.1349664
Open Access Y


Rusch, Thomas (Details)
Hornik, Kurt (Details)
Mair, Patrick (Harvard, United States/USA)
Competence Center for Empirical Research Methods WE (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1162 Statistics (Details)
5509 Psychological methodology (Details)
5701 Applied statistics (Details)
5704 Social statistics (Details)
5912 Social sciences (interdisciplinary) (Details)
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