Generalized density clustering

Abstract

We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based methods for choosing the bandwidth and we study the stability properties of density clusters. We show that a simple graph-based algorithm successfully approximates the high density clusters.

Published in at http://dx.doi.org/10.1214/10-AOS797 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Fast learning rates for plug-in classifiers
• Uniform in bandwidth consistency of kernel-type function estimators
• Empirical graph Laplacian approximation of Laplace--Beltrami operators: Large sample results
• Generalization error bounds in semi-supervised classification under the cluster assumption
• Adaptive Hausdorff estimation of density level sets

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• Asymptotics of Lower Dimensional Zero-Density Regions
• Improving Spectral Clustering using the Asymptotic Value of the Normalised Cut