Recent results on heat kernel embedding of graphs

Abstract

This paper describes how heat-kernel asymptotics can be used to compute approximate Euclidean distances between nodes in a graph. The distances are used to embed the graph-nodes in a low-dimensional space by performing Multidimensional Scaling(MDS). We perform an analysis of the distances, and demonstrate that they are related to the sectional curvature of the connecting geodesic on the manifold. Experiments with moment invariants computed from the embedded points show that they can be used for graph clustering. © Springer-Verlag Berlin Heidelberg 2005.