Simple Hierarchical PageRank Graph Neural Networks

Abstract Graph neural networks (GNNs) have many variants for graph representation learning. Several works introduce PageRank into GNNs to improve its neighborhood aggregation capabilities. However, these methods leverage the general PageRank to perform complex neighborhood aggregation to obtain the final feature representation, which leads to high computational cost and oversmoothing. In this paper, we propose simple hierarchical PageRank graph neural networks (SHP-GNNs), which first utilize the simple PageRank to aggregate different neighborhood ranges of each node, and then leverage a jumping architecture to combine these aggregated features to enable hierarchical structure-aware representation. In this case, first, the simple PageRank turns the neighborhood aggregation process to no-learning, thereby reducing the computational complexity of the model. Then, the jumping structure combines the aggregation features of each node's different hierarchy (neighborhood range) to learn more informative feature representation. Finally, the successful combination of the above methods alleviate the oversmoothing problem of deep GNNs. Our experimental evaluation demonstrates that SHP-GNNs achieve or match state-of-the-art results in node classification tasks, text classification tasks, and community prediction tasks. Moreover, since SHP-GNNs' neighborhood aggregation is a no-learning process, SHP-GNNs are successfully extended to node clustering tasks.