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.

翻译：我们研究了多路复用图嵌入问题，即节点通过多种关系类型（维度）进行交互的图。近年来，已有多种方法被提出以解决该问题。然而，随着具有异构特征的图数据不断涌现，对更有效且专门化方法的需求日益增长。特别地，现实中的多路复用图可能呈现高维特性，这使得构建单一共识表示变得困难。此外，重要信息可能隐藏于散落在多个维度中的复杂潜在结构里。为解决这些问题，我们提出HMGE——一种基于分层聚合的高维多路复用图新颖嵌入方法。分层聚合通过学习图维度的层次化组合，并在每个层级细化嵌入表示。非线性组合基于前一层级计算，从而揭示隐藏在多路复用图维度中的复杂信息与潜在结构。此外，我们利用局部块与全局摘要之间的互信息最大化来无监督训练模型，这有助于捕获分布在图不同位置的全局相关特征。在合成数据与真实数据上的详细实验表明，我们的方法适用于链接预测与节点分类等下游监督任务。