Joint Adaptive Feature Smoothing and Topology Extraction via Generalized PageRank GNNs

In many important applications, the acquired graph-structured data includes both node features and graph topology information. Graph neural networks (GNNs) are able to accurately process both the feature signals and graph topology individually. Nevertheless, they face the problem of trading-off the benefits of a shallow network architecture and deep multi-step information propagation when attempting to optimize their learning performance using both data components. Most existing GNN implementations based on node feature propagation are shallow due to the fact that a large number of propagation steps leads to feature over-smoothing and hence diminishes their discriminative power. In contrast, when processing topological information, it is common to use label propagation and PageRank methods that require a large number of message passing steps. We address these two contradictory requirements by combining GNNs with an adaptive generalized PageRank (GPR) scheme in a model termed GPR-GNN. GPR-GNN is the first known architecture that not only provably mitigates feature over-smoothing but also adaptively learns the weights of the GPR model to optimize topological information extraction. Our theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the contextual stochastic block model. We also compare the performance of our NN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using nine well-known benchmark datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.