1 research outputs found
Estimating Vector Fields on Manifolds and the Embedding of Directed Graphs
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. In the process, we also obtain new theoretical results on the
limits of "Laplacian type" matrices derived from directed graphs. The
application of our method to both artificially constructed and real data
highlights its strengths.Comment: 16 page