# How the result of graph clustering methods depends on the construction of the graph

• Volume: 17, page 370-418
• ISSN: 1292-8100

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## Abstract

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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 clustering 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 clustering 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.

## How to cite

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Maier, Markus, von Luxburg, Ulrike, and Hein, Matthias. "How the result of graph clustering methods depends on the construction of the graph." ESAIM: Probability and Statistics 17 (2013): 370-418. <http://eudml.org/doc/273621>.

@article{Maier2013,
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 clustering 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 clustering 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.},
author = {Maier, Markus, von Luxburg, Ulrike, Hein, Matthias},
journal = {ESAIM: Probability and Statistics},
keywords = {random geometric graph; clustering; graph cuts; random geometric graphs},
language = {eng},
pages = {370-418},
publisher = {EDP-Sciences},
title = {How the result of graph clustering methods depends on the construction of the graph},
url = {http://eudml.org/doc/273621},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Maier, Markus
AU - von Luxburg, Ulrike
AU - Hein, Matthias
TI - How the result of graph clustering methods depends on the construction of the graph
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 370
EP - 418
AB - 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 clustering 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 clustering 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.
LA - eng
KW - random geometric graph; clustering; graph cuts; random geometric graphs
UR - http://eudml.org/doc/273621
ER -

## References

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