Statistical embedding for directed graphs

We propose a novel statistical node embedding of directed graphs, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density function over a measurable real n-dimensional space. Furthermore, we analyze the connection to the geometrical properties of such embedding and characterize the curvature of the statistical manifolds. Extensive experiments show that our proposed embedding is better preserving the global geodesic information of graphs, as well as outperforming existing embedding models on directed graphs in a variety of evaluation metrics, in an unsupervised setting.