Constrained Heat Kernel Graph Diffusion Convolution: A High-Dimensional Statistical Approximation via Information Theory

Graph neural networks have been widely applied in various domains, handling numerous entities with high-dimensional features. Their success largely stems from the powerful information propagation process. Among these networks, diffusion-based approaches, such as generalized graph diffusion convolution, have extended conventional immediate neighborhood aggregation function to a diffusion process based on Newton’s law of cooling. Despite substantial improvements in model performance, the diffusion time is obtained by either grid search or complex bi-level optimization on train and validation sets. Furthermore, these methods do not explicitly explain the diffusion time obtained from the specific graph data. We propose the Constrained Heat Kernel Graph Diffusion to address these issues to estimate the appropriate diffusion time based on information theory and moments. By conceptualizing the graph as a communication network, we approximate the diffusion process as the transmission and reception of graph signals over noisy channels bounded by the channel capacity. Our method demonstrates consistent performance improvements in downstream graph-mining tasks across six public datasets, offering a principled framework and faster approximation method for the diffusion time. The results from the ablation study further validate the effectiveness of the proposed method.