A Graph Embedding Method Using the Jensen-Shannon Divergence

Riesen and Bunke recently proposed a novel dissimilarity based approach for embedding graphs into a vector space. One drawback of their approach is the computational cost graph edit operations required to compute the dissimilarity for graphs. In this paper we explore whether the Jensen-Shannon divergence can be used as a means of computing a fast similarity measure between a pair of graphs. We commence by computing the Shannon entropy of a graph associated with a steady state random walk. We establish a family of prototype graphs by using an information theoretic approach to construct generative graph prototypes. With the required graph entropies and a family of prototype graphs to hand, the Jensen-Shannon divergence between a sample graph and a prototype graph can be computed. It is defined as the Jensen-Shannon between the pair of separate graphs and a composite structure formed by the pair of graphs. The required entropies of the graphs can be efficiently computed, the proposed graph embedding using the Jensen-Shannon divergence avoids the burdensome graph edit operation. We explore our approach on several graph datasets abstracted from computer vision and bioinformatics databases.