  We propose a novel node embedding of directed graphs to statistical
manifolds, 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 space. Furthermore, we analyze
the connection between the geometrical properties of such embedding and their
efficient learning procedure. Extensive experiments show that our proposed
embedding is better in 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.
