Recently, one has seen a surge of interest in developing such methods
including ones for learning such representations for (undirected) graphs (while
preserving important properties). However, most of the work to date on
embedding graphs has targeted undirected networks and very little has focused
on the thorny issue of embedding directed networks. In this paper, we instead
propose to solve the directed graph embedding problem via a two-stage approach:
in the first stage, the graph is symmetrized in one of several possible ways,
and in the second stage, the so-obtained symmetrized graph is embedded using
any state-of-the-art (undirected) graph embedding algorithm. Note that it is
not the objective of this paper to propose a new (undirected) graph embedding
algorithm or discuss the strengths and weaknesses of existing ones; all we are
saying is that whichever be the suitable graph embedding algorithm, it will fit
in the above proposed symmetrization framework.

该研究探索了一种针对有向图嵌入问题的两阶段方法，第一阶段对图进行对称化处理，第二阶段使用任何先进的（无向）图嵌入算法来嵌入所获得的对称图。

对称化有向图嵌入

Symmetrization for Embedding Directed Graphs

Directed graphs have been widely used in Community Question Answering
services (CQAs) to model asymmetric relationships among different types of
nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is
an essential property of directed graphs, since it can play an important role
in downstream graph inference and analysis. Question difficulty and user
expertise follow the characteristic of asymmetric transitivity. Maintaining
such properties, while reducing the graph to a lower dimensional vector
embedding space, has been the focus of much recent research. In this paper, we
tackle the challenge of directed graph embedding with asymmetric transitivity
preservation and then leverage the proposed embedding method to solve a
fundamental task in CQAs: how to appropriately route and assign newly posted
questions to users with the suitable expertise and interest in CQAs. The
technique incorporates graph hierarchy and reachability information naturally
by relying on a non-linear transformation that operates on the core
reachability and implicit hierarchy within such graphs. Subsequently, the
methodology levers a factorization-based approach to generate two embedding
vectors for each node within the graph, to capture the asymmetric transitivity.
Extensive experiments show that our framework consistently and significantly
outperforms the state-of-the-art baselines on two diverse real-world tasks:
link prediction, and question difficulty estimation and expert finding in
online forums like Stack Exchange. Particularly, our framework can support
inductive embedding learning for newly posted questions (unseen nodes during
training), and therefore can properly route and assign these kinds of questions
to experts in CQAs.

本文提出了一个方法来维护有向图的不对称性传递性质，基于所提出的算法可以将问题正确分配给具有相应专业技能的用户，并在各项指标上都表现优异，支持对未来问题的嵌入学习