How Powerful is Implicit Denoising in Graph Neural Networks
This work addresses a fundamental gap in analyzing noise removal in GNNs, which is crucial for improving robustness in graph-based machine learning applications, though it is incremental as it builds on existing denoising concepts.
The paper tackles the problem of understanding implicit denoising in Graph Neural Networks (GNNs) by conducting a theoretical analysis that identifies factors like connectivity and architecture, and proposes a robust graph convolution method that enhances denoising, with empirical evaluations confirming effectiveness.
Graph Neural Networks (GNNs), which aggregate features from neighbors, are widely used for graph-structured data processing due to their powerful representation learning capabilities. It is generally believed that GNNs can implicitly remove the non-predictive noises. However, the analysis of implicit denoising effect in graph neural networks remains open. In this work, we conduct a comprehensive theoretical study and analyze when and why the implicit denoising happens in GNNs. Specifically, we study the convergence properties of noise matrix. Our theoretical analysis suggests that the implicit denoising largely depends on the connectivity, the graph size, and GNN architectures. Moreover, we formally define and propose the adversarial graph signal denoising (AGSD) problem by extending graph signal denoising problem. By solving such a problem, we derive a robust graph convolution, where the smoothness of the node representations and the implicit denoising effect can be enhanced. Extensive empirical evaluations verify our theoretical analyses and the effectiveness of our proposed model.