Commute times for graph spectral clustering

Abstract

This paper exploits the properties of the commute time to develop a graph-spectral method for image segmentation. Our starting point is the lazy random walk on the graph, which is determined by the heat-kernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterise the random walk using the commute time between nodes, and show how this quantity may be computed from the Laplacian spectrum using the discrete Green's function. We explore the application of the commute time for image segmentation using the eigenvector corresponding to the smallest eigenvalue of the commute time matrix. © Springer-Verlag Berlin Heidelberg 2005.