  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.
