GCN-MPPR: Enhancing the Propagation of Message Passing Neural Networks via Motif-Based Personalized PageRank

The algorithms based on message passing neural networks (MPNNs) on graphs have recently achieved great success for various graph applications. However, studies find that these methods always propagate the information to very limited neighborhoods with shallow depth, particularly due to over-smoothing. That means most of the existing MPNNs fail to be so `deep'. Although some previous work tended to handle this challenge via optimization- or structure-level remedies, the overall performance of GCNs still suffers from limited accuracy, poor stability, and unaffordable computational cost. Moreover, neglect of higher-order relationships during the propagation of MPNNs has further limited the performance of them. To overcome these challenges, a novel variant of PageRank named motif-based personalized PageRank (MPPR) is proposed to measure the influence of one node to another on the basis of considering higher-order motif relationships. Secondly, the MPPR is utilized to the message passing process of GCNs, thereby guiding the message passing process at a relatively `high' level. The experimental results show that the proposed method outperforms almost all of the baselines on accuracy, stability, and time consumption. Additionally, the proposed method can be considered as a component that can underpin almost all GCN tasks, with DGCRL being demonstrated in the experiment. The anonymous code repository is available at: https://anonymous.4open.science/r/GCN-MPPR-AFD6/.