Measuring Graph Similarity Using Spectral Geometry

In this paper we study the manifold embedding of graphs resulting from the Young-Householder decomposition of the heat kernel [19]. We aim to explore how the sectional curvature associated with the embedding can be used as feature for the purposes of gauging the similarity of graphs, and hence clustering them. To gauging the similarity of pairs of graphs, we require a means of comparing sets of such features without explicit correspondences between the nodes of the graphs being considered. To this end, the Hausdorff distance, and a robust modified variant of the Hausdorff distance are used. we experiment on sets of graphs representing the proximity image features in different views of different objects. By applying multidimensional scaling to the Hausdorff distances between the different object views, we demonstrate that our sectional curvature representation is capable of clustering the different views of the same object together.