# Structural Hierarchy-Enhanced Network Representation Learning
## 1 Introduction  
Network representation learning (NRL) is a crucial task in social and information network analysis. The idea of NRL is to learn a mapping function that converts each node into a low-dimensional embedding space while preserving the structural proximity between nodes in the given network. The derived node embedding vectors can be utilized for downstream tasks, including node classification, link prediction, and community detection. Typical NRL methods include DeepWalk [1], LINE [2], and node2 vec [3], which consider structural neighborhood to depict every node. Metapath2 vec [4] extends the skip-gram based NRL to heterogeneous information networks that contain multiple types of nodes and links. DANE [5] incorporates the similarity between node attributes into NRL. GCN [6] further learns node embeddings for semi-supervised node classification through a layer-wise propagation with graph convolution. Regarding the typical NRL approaches [1; 2; 3] that preserve structural proximity in node embeddings, we think there are two major insufficiencies. First, every node is only aware of its few-hop neighbors by random walk sampling, which push them to be close in the embedding space. Nevertheless, as illustrated in the general node embedding space in Figure 1, non-neighbor nodes (\(v_{5}\)) being pushed away by negative sampling could still have some connections with the target node (\(v_{1}\)), e.g., belonging to the same network community (C1). In addition, neighbor nodes (\(v_{8}\)) sampled by random walks being pushed together could have weak connections to the target node (\(v_{1}\)), e.g., belonging to different communities (C1 and C3). In other words, community-level information cannot be incorporated into the learning of node embeddings. We think network communities can inform nodes to better recognize which nodes should better push together and away, as shown in thecommunity-aware embedding space in Figure 1. Second, the given graph depicts only the fine-grained interactions between nodes. As shown in Figure 1, the given graph is a collaboration network, and thus the links depict co-authorships. The coarse-grained semantics, including how authors involve in different research areas and belong to different institutes, together with their interactions, is not aware by typical NRL approaches. We think encoding coarse-grained semantics can improve the effectiveness of node embeddings. In this paper, we propose a novel framework, Structural Hierarchy Enhancement (SHE), to enhance the effectiveness of network representation learning. The main idea is two-fold. First, we construct a structural hierarchy that depicts both fine-grained and coarse-grained semantics of nodes and their interactions. We consider that node semantics is depicted by communities (i.e., clusters of nodes), and thus utilize community detection techniques to produce the structural hierarchy. By learning the embeddings of nodes in different levels of the hierarchy, our model will be capable of encoding multiple different views of each node. Hence, the semantics of nodes can be enriched, and nodes can be better distinguished from one another in the embedding space. Second, we utilize such a hierarchy to enhance NRL. Our SHE can be seamlessly applied to enhance any of existing typical NRL models mentioned above. Besides, any existing and state-of-the-art hierarchical community detection algorithm can be applied to generate the hierarchy. In other words, our SHE model provides great flexibility to be compatible with different combinations of NRL methods and community detection techniques. **Related Work. ** The most relevant studies are HARP [7] and Marc [8], which are hierarchical NRL methods. HARP collapses nodes according to edge and star connections so that the hierarchy can be constructed for NRL. Marc iteratively consider 3-cliques as super nodes to construct the hierarchy. However, community knowledge in networks is not considered in both HARP and Marc.