Marc: Multi-Granular Representation Learning for Networks Based on the 3-Clique

Network embedding is of paramount importance in many real applications, such as node classification, network visualization, and link prediction. Existing methods can effectively encode different structural properties into representations. Most of them are single-granular representation learning methods that do not enable the network to be easily analyzed at various scales. There are many kinds of hierarchical structures in reality. In this paper, we propose a novel algorithm multi-granular representation learning for networks based on the 3-clique named Marc. It makes the representations of the current network be formed by both considering the structure of this granular network and inheriting the coarser network representation results. Firstly, we propose the 3-clique coarsening strategy. A 3-clique is coarsened to be a supernode in the coarser network. These coarsened networks with different granularities, preserve the original network's main structure. Secondly, we use the single-granular optimization objective function to obtain the nodes' representations of each granular network. Finally, the refinement model learns the nodes' representations, starting from the coarsest network. The learned representations of supernodes serve as good initializations for embedding the corresponding coarsened nodes from the finer network. This process is repeated until we obtain an embedding for each node in the original network which preserves the relationship among multi-granular networks. The experimental results on five public datasets, Wiki, BlogCatalog, Cora, CiteSeer, and DBLP, demonstrate that Marc has a better Macro F1 value for classification tasks than the baseline methods.