We investigate the problem of multiplex graph embedding, that is, graphs in
which nodes interact through multiple types of relations (dimensions). In
recent years, several methods have been developed to address this problem.
However, the need for more effective and specialized approaches grows with the
production of graph data with diverse characteristics. In particular,
real-world multiplex graphs may exhibit a high number of dimensions, making it
difficult to construct a single consensus representation. Furthermore,
important information can be hidden in complex latent structures scattered in
multiple dimensions. To address these issues, we propose HMGE, a novel
embedding method based on hierarchical aggregation for high-dimensional
multiplex graphs. Hierarchical aggregation consists of learning a hierarchical
combination of the graph dimensions and refining the embeddings at each
hierarchy level. Non-linear combinations are computed from previous ones, thus
uncovering complex information and latent structures hidden in the multiplex
graph dimensions. Moreover, we leverage mutual information maximization between
local patches and global summaries to train the model without supervision. This
allows to capture of globally relevant information present in diverse locations
of the graph. Detailed experiments on synthetic and real-world data illustrate
the suitability of our approach to downstream supervised tasks, including link
prediction and node classification.

我们提出了 HMGE，一种基于分层聚合的高维多重图嵌入方法，通过学习图维度的分层组合和在每个层次进行嵌入的方式，揭示了多重图维度中隐藏的复杂信息和潜在结构，并通过局部补丁和全局摘要之间的互信息最大化来训练模型以捕捉图中处于不同位置但具有全局相关信息的能力。通过在合成和现实世界数据上进行的详细实验，我们证明了我们的方法在链接预测和节点分类等下游有监督任务中的适用性。