Efficient Identity and Position Graph Embedding via Spectral-Based Random Feature Aggregation

Graph neural networks (GNNs), which capture graph structures via a feature aggregation mechanism following the graph embedding framework, have demonstrated a powerful ability to support various tasks. According to the topology properties (e.g., structural roles or community memberships of nodes) to be preserved, graph embedding can be categorized into identity and position embedding. However, it is unclear for most GNN-based methods which property they can capture. Some of them may also suffer from low efficiency and scalability caused by several time- and space-consuming procedures (e.g., feature extraction and training). From a perspective of graph signal processing, we find that high- and low-frequency information in the graph spectral domain may characterize node identities and positions, respectively. Based on this investigation, we propose random feature aggregation (RFA) for efficient identity and position embedding, serving as an extreme ablation study regarding GNN feature aggregation. RFA (i) adopts a spectral-based GNN without learnable parameters as its backbone, (ii) only uses random noises as inputs, and (iii) derives embeddings via just one feed-forward propagation (FFP). Inspired by degree-corrected spectral clustering, we further introduce a degree correction mechanism to the GNN backbone. Surprisingly, our experiments demonstrate that two variants of RFA with high- and low-pass filters can respectively derive informative identity and position embeddings via just one FFP (i.e., without any training). As a result, RFA can achieve a better trade-off between quality and efficiency for both identity and position embedding over various baselines.