In existing graph data, the connection relationships often exhibit uniform weights, leading to the model aggregating neighboring nodes with equal weights across various connection types. However, this uniform aggregation of diverse information diminishes the discriminability of node representations, contributing significantly to the over-smoothing issue in models. In this paper, we propose the Flexible Graph Neural Diffusion (FGND) model, incorporating latent class representation to address the misalignment between graph topology and node features. In particular, we combine latent class representation learning with the inherent graph topology to reconstruct the diffusion matrix during the graph diffusion process. We introduce the sim metric to quantify the degree of mismatch between graph topology and node features. By flexibly adjusting the dependency level on node features through the hyperparameter, we accommodate diverse adjacency relationships. The effective filtering of noise in the topology also allows the model to capture higher order information, significantly alleviating the over-smoothing problem. Meanwhile, we model the graphical diffusion process as a set of differential equations and employ advanced partial differential equation tools to obtain more accurate solutions. Empirical evaluations on five benchmarks reveal that our FGND model outperforms existing popular GNN methods in terms of both overall performance and stability under data perturbations. Meanwhile, our model exhibits superior performance in comparison to models tailored for heterogeneous graphs and those designed to address oversmoothing issues.

Graph convolutional neural network (GCN) is a powerful deep learning framework for network data. However, variants of graph neural architectures can lead to drastically different performance on different tasks. Model comparison calls for a unifying framework with interpretability and principled experimental procedures. Based on the theories from graph signal processing (GSP), we show that GCN’s capability is fundamentally limited by the uncertainty principle, and wavelets provide a controllable trade-off between local and global information. We adapt wavelet denoising filters to the graph domain, unifying popular variants of GCN under a common interpretable mathematical framework. Furthermore, we propose WaveThresh and WaveShrink which are novel GCN models based on proven denoising filters from the signal processing literature. Empirically, we evaluate our models and other popular GCNs under a more principled procedure and analyze how trade-offs between local and global graph signals can lead to better performance in different datasets.