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Conference Paper

Pruning nearest neighbor cluster trees

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84024

Kpotufe,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons76237

von Luxburg,  U
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Kpotufe, S., & von Luxburg, U. (2011). Pruning nearest neighbor cluster trees. In 28th International Conference on Machine Learning (ICML 2011) (pp. 225-232). Madison, WI, USA: International Machine Learning Society.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-BB2A-E
Abstract
Nearest neighbor (k-NN) graphs are widely used in machine learning and data mining applications, and our aim is to better understand what they reveal about the cluster structure of the unknown underlying distribution of points. Moreover, is it possible to identify spurious structures that might arise due to sampling variability? Our first contribution is a statistical analysis that reveals how certain subgraphs of a k-NN graph form a consistent estimator of the cluster tree of the underlying distribution of points. Our second and perhaps most important contribution is the following finite sample guarantee. We carefully work out the tradeoff between aggressive and conservative pruning and are able to guarantee the removal of all spurious cluster structures while at the same time guaranteeing the recovery of salient clusters. This is the first such finite sample result in the context of clustering.