  Graph representation learning has demonstrated improved performance in tasks
such as link prediction and node classification across a range of domains.
Research has shown that many natural graphs can be organized in hierarchical
communities, leading to approaches that use these communities to improve the
quality of node representations. However, these approaches do not take
advantage of the learned representations to also improve the quality of the
discovered communities and establish an iterative and joint optimization of
representation learning and community discovery. In this work, we present Mazi,
an algorithm that jointly learns the hierarchical community structure and the
node representations of the graph in an unsupervised fashion. To account for
the structure in the node representations, Mazi generates node representations
at each level of the hierarchy, and utilizes them to influence the node
representations of the original graph. Further, the communities at each level
are discovered by simultaneously maximizing the modularity metric and
minimizing the distance between the representations of a node and its
community. Using multi-label node classification and link prediction tasks, we
evaluate our method on a variety of synthetic and real-world graphs and
demonstrate that Mazi outperforms other hierarchical and non-hierarchical
methods.
