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Assessing and quantifying clusteredness: The OPTICS Cordillera

Rusch, Thomas and Hornik, Kurt and Mair, Patrick (2017) Assessing and quantifying clusteredness: The OPTICS Cordillera. Journal of Computational and Graphical Statistics. ISSN 1537-2715

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Abstract

This paper 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 neighbouring 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).

Item Type: Article
Additional Information: This is the accepted author Version, it will be removed once the edited and final typeset version is posted online. (http://www.tandfonline.com/action/authorSubmission?journalCode=ucgs20&page=instructions)
Keywords: index, cluster analysis, dimensionality reduction, perception
Divisions: Kompetenzzentren > Empirische Forschungsmethoden
Version of the Document: Accepted for Publication
Depositing User: Gertraud Novotny
Date Deposited: 05 Sep 2017 12:36
Last Modified: 05 Sep 2017 13:07
Related URLs:
FIDES Link: https://bach.wu.ac.at/d/research/results/82040/
URI: http://epub.wu.ac.at/id/eprint/5725

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