Hierarchical Position Embedding of Graphs with Landmarks and Clustering for Link Prediction

Learning positional information of nodes in a graph is important for link prediction tasks. We propose a representation of positional information using representative nodes called landmarks. A small number of nodes with high degree centrality are selected as landmarks, which serve as reference points for the nodes' positions. We justify this selection strategy for well-known random graph models and derive closed-form bounds on the average path lengths involving landmarks. In a model for power-law graphs, we prove that landmarks provide asymptotically exact information on inter-node distances. We apply theoretical insights to practical networks and propose Hierarchical Position embedding with Landmarks and Clustering (HPLC). HPLC combines landmark selection and graph clustering, where the graph is partitioned into densely connected clusters in which nodes with the highest degree are selected as landmarks. HPLC leverages the positional information of nodes based on landmarks at various levels of hierarchy such as nodes' distances to landmarks, inter-landmark distances and hierarchical grouping of clusters. Experiments show that HPLC achieves state-of-the-art performances of link prediction on various datasets in terms of HIT@K, MRR, and AUC. The code is available at \url{https://github.com/kmswin1/HPLC}.

ComDensE : Combined Dense Embedding of Relation-aware and Common Features for Knowledge Graph Completion

Real-world knowledge graphs (KG) are mostly incomplete. The problem of recovering missing relations, called KG completion, has recently become an active research area. Knowledge graph (KG) embedding, a low-dimensional representation of entities and relations, is the crucial technique for KG completion. Convolutional neural networks in models such as ConvE, SACN, InteractE, and RGCN achieve recent successes. This paper takes a different architectural view and proposes ComDensE which combines relation-aware and common features using dense neural networks. In the relation-aware feature extraction, we attempt to create relational inductive bias by applying an encoding function specific to each relation. In the common feature extraction, we apply the common encoding function to all input embeddings. These encoding functions are implemented using dense layers in ComDensE. ComDensE achieves the state-of-the-art performance in the link prediction in terms of MRR, HIT@1 on FB15k-237 and HIT@1 on WN18RR compared to the previous baseline approaches. We conduct an extensive ablation study to examine the effects of the relation-aware layer and the common layer of the ComDensE. Experimental results illustrate that the combined dense architecture as implemented in ComDensE achieves the best performance.