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.