Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. A single GNN layer typically consists of a feature transformation and a feature aggregation operation. The former normally uses feed-forward networks to transform features, while the latter aggregates the transformed features over the graph. Numerous recent works have proposed GNN models with different designs in the aggregation operation. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models including GCN, GAT, PPNP, and APPNP can be regarded as (approximately) solving a graph denoising problem with a smoothness assumption. Such a unified view across GNNs not only provides a new perspective to understand a variety of aggregation operations but also enables us to develop a unified graph neural network framework UGNN. To demonstrate its promising potential, we instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes. Comprehensive experiments show the effectiveness of ADA-UGNN.

本篇论文针对图结构数据的表征学习中的聚合操作进行研究，探究GCN、GAT、PPNP、APPNP等GNN模型的聚合过程与图像去噪问题之间的通用性，进而提出统一图神经网络框架UGNN，并基于此开发了ADA-UGNN模型，通过实验验证了其在自适应平滑性的图中的有效性。

图神经网络作为图信号去噪的统一视角