Graph Embedding Using Commute Time

Huaijun Qiu, Edwin R. Hancock

Abstract: This paper explores the use of commute-time preserving embedding as means of data-clustering. Commute time is a measure of the time taken for a random walk to set-out and return between a pair of nodes on a graph. It may be computed from the spectrum of the Laplacian matrix. Since the commute time is averaged over all potential paths between a pair of nodes, it is potentially robust to variations in graph structure due to edge insertions or deletions. Here we demonstrate how nodes of a graph can be embedded in a vector space in a manner that preserves commute time. We present a number of important properties of the embedding. We experiment with the method for separating object motions in image sequences.