PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

On the Convergence of Spectral Clustering on Random Samples: The Normalized Case
Ulrike von Luxburg, Olivier Bousquet and Mikhail Belkin
In: COLT 2004, 1-4 July 2004, Banff, Canada.


Given a set of n randomly drawn sample points, spectral clustering in its simplest form uses the second eigenvector of the graph Laplacian matrix, constructed on the similarity graph between the sample points, to obtain a partition of the sample. We are interested in the question how spectral clustering behaves for growing sample size n. In case one uses the normalized graph Laplacian, we show that spectral clustering usually converges to an intuitively appealing limit partition of the data space. We argue that in case of the unnormalized graph Laplacian, equally strong convergence results are difficult to obtain.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:404
Deposited By:Ulrike Von Luxburg
Deposited On:19 December 2004