PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

How the result of graph clustering methods depends on the construction of the graph
Markus Maier, Ulrike v. Luxburg and Matthias Hein
ESAIM Probablitiy and Statistics 2011.

Abstract

We study the scenario of graph-based clustering algorithms such as spectral clustering. Given a set of data points, one first has to construct a graph on the data points and then apply a graph clustering algorithm to find a suitable partition of the graph. Our main question is if and how the construction of the graph (choice of the graph, choice of parameters, choice of weights) influences the outcome of the final clus- tering result. To this end we study the convergence of cluster quality measures such as the normalized cut or the Cheeger cut on various kinds of random geometric graphs as the sample size tends to infinity. It turns out that the limit values of the same objective function are systematically different on different types of graphs. This implies that clus- tering results systematically depend on the graph and can be very different for different types of graph. We provide examples to illustrate the implications on spectral clustering.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8636
Deposited By:Ulrike Von Luxburg
Deposited On:16 February 2012