Abstract

Clustering nodes in a graph is a useful general technique in data mining of large network data sets. In this context, Newman and Girvan [9] recently proposed an objective function for graph clustering called the Q function which allows automatic selection of the number of clusters. Empirically, higher values of the Q function have been shown to correlate well with good graph clusterings. In this paper we show how optimizing the Q function can be reformulated as a spectral relaxation problem and propose two new spectral clustering algorithms that seek to maximize Q. Experimental results indicate that the new algorithms are e#cient and e#ective at finding both good clusterings and the appropriate number of clusters across a variety of real-world graph data sets. In addition, the spectral algorithms are much faster for large sparse graphs, scaling roughly linearly with the number of nodes n in the graph, compared to O(n ) for previous clustering algorithms using the Q function.

Citations