  Graph embedding is a central problem in social network analysis and many
other applications, aiming to learn the vector representation for each node.
While most existing approaches need to specify the neighborhood and the
dependence form to the neighborhood, which may significantly degrades the
flexibility of representation, we propose a novel graph node embedding method
(namely GESF) via the set function technique. Our method can 1) learn an
arbitrary form of representation function from neighborhood, 2) automatically
decide the significance of neighbors at different distances, and 3) be applied
to heterogeneous graph embedding, which may contain multiple types of nodes.
Theoretical guarantee for the representation capability of our method has been
proved for general homogeneous and heterogeneous graphs and evaluation results
on benchmark data sets show that the proposed GESF outperforms the
state-of-the-art approaches on producing node vectors for classification tasks.
