Graph Denoising with Framelet Regularizer
This addresses robustness issues in graph neural networks for real-world applications, though it is incremental as it builds on existing denoising methods.
The paper tackles the problem of noise in graph data by proposing a denoising scheme with framelet regularizers for both feature and structure, achieving significantly better performance compared to popular graph convolutions, especially under heavy contamination.
As graph data collected from the real world is merely noise-free, a practical representation of graphs should be robust to noise. Existing research usually focuses on feature smoothing but leaves the geometric structure untouched. Furthermore, most work takes L2-norm that pursues a global smoothness, which limits the expressivity of graph neural networks. This paper tailors regularizers for graph data in terms of both feature and structure noises, where the objective function is efficiently solved with the alternating direction method of multipliers (ADMM). The proposed scheme allows to take multiple layers without the concern of over-smoothing, and it guarantees convergence to the optimal solutions. Empirical study proves that our model achieves significantly better performance compared with popular graph convolutions even when the graph is heavily contaminated.