Graph Distributional Signals for Regularization in Graph Neural Networks

In graph neural networks (GNNs), both node features and labels are examples of graph signals. While it is common in graph signal processing to impose signal smoothness constraints in learning and estimation tasks, it is unclear how this can be done for discrete node labels. We bridge this gap by introducing the concept of graph distributional signals. We work with the distributions of node labels instead of their values and propose notions of smoothness and non-uniformity of such graph distributional signals. We then propose a general regularization method for GNNs that allows us to encode distributional smoothness and non-uniformity of the model output in semi-supervised node classification tasks. Numerical experiments demonstrate that our method can significantly improve the performance of most base GNN models in different problem settings.