A Unified View on Graph Neural Networks as Graph Signal Denoising

TL;DR

This paper presents a unified theoretical framework viewing various GNN aggregation methods as graph signal denoising, leading to a new adaptable GNN model that improves performance on graphs with varying smoothness.

Contribution

It unifies the understanding of different GNN aggregation techniques as graph denoising and introduces a new adaptable GNN model, ADA-UGNN.

Findings

Unified view enhances understanding of GNNs' aggregation processes.

ADA-UGNN outperforms existing models on graphs with varying smoothness.

The framework enables development of more flexible GNN architectures.

Abstract

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.