Estimating Vector Fields on Manifolds and the Embedding of Directed Graphs

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This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information.

• We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.
• This is the first generative model of its kind for directed graphs.
• We introduce a graph embedding algorithm that estimates all three features of this model: the low-dimensional embedding of the manifold, the data density and the vector field.