RaWaNet: Enriching Graph Neural Network Input via Random Walks on Graphs
This addresses the need for more effective graph representations in molecular learning, though it is incremental as it builds on existing GNN frameworks.
The paper tackles the problem of limited input descriptors for graph neural networks (GNNs) by enriching inputs with random walks of selected lengths and their stationary distributions, resulting in a shallow network outperforming deep GNNs on molecular datasets without using edge features.
In recent years, graph neural networks (GNNs) have gained increasing popularity and have shown very promising results for data that are represented by graphs. The majority of GNN architectures are designed based on developing new convolutional and/or pooling layers that better extract the hidden and deeper representations of the graphs to be used for different prediction tasks. The inputs to these layers are mainly the three default descriptors of a graph, node features $(X)$, adjacency matrix $(A)$, and edge features $(W)$ (if available). To provide a more enriched input to the network, we propose a random walk data processing of the graphs based on three selected lengths. Namely, (regular) walks of length 1 and 2, and a fractional walk of length $γ\in (0,1)$, in order to capture the different local and global dynamics on the graphs. We also calculate the stationary distribution of each random walk, which is then used as a scaling factor for the initial node features ($X$). This way, for each graph, the network receives multiple adjacency matrices along with their individual weighting for the node features. We test our method on various molecular datasets by passing the processed node features to the network in order to perform several classification and regression tasks. Interestingly, our method, not using edge features which are heavily exploited in molecular graph learning, let a shallow network outperform well known deep GNNs.