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Stability-Based Validation of Clustering Solutions

tilman.lange{at}info.ethz.ch, Swiss Federal Institute of Technology (ETH) Zurich, Institute for Computational Science, CH-8092 Zurich, Switzerland

Volker Roth

volker.roth{at}info.ethz.ch, Swiss Federal Institute of Technology (ETH) Zurich, Institute for Computational Science, CH-8092 Zurich, Switzerland

Mikio L. Braun

braunm{at}cs.uni-bonn.de, Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Informatik III, 53117 Bonn, Germany

Joachim M. Buhmann

jbuhmann{at}info.ethz.ch, Swiss Federal Institute of Technology (ETH) Zurich, Institute for Computational Science, CH-8092 Zurich, Switzerland

Data clustering describes a set of frequently employed techniques in exploratory data analysis to extract "natural" group structure in data. Such groupings need to be validated to separate the signal in the data from spurious structure. In this context, finding an appropriate number of clusters is a particularly important model selection question. We introduce a measure of cluster stability to assess the validity of a cluster model. This stability measure quantifies the reproducibility of clustering solutions on a second sample, and it can be interpreted as a classification risk with regard to class labels produced by a clustering algorithm. The preferred number of clusters is determined by minimizing this classification risk as a function of the number of clusters. Convincing results are achieved on simulated as well as gene expression data sets. Comparisons to other methods demonstrate the competitive performance of our method and its suitability as a general validation tool for clustering solutions in real-world problems.

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