Graph Aggregating-Repelling Network: Do Not Trust All Neighbors in Heterophilic Graphs.

Area of Science:

• Machine Learning
• Graph Theory
• Network Analysis

Background:

• Graph Neural Networks (GNNs) excel on homophilic graphs but struggle with heterophilic graphs where nodes have dissimilar features.
• Existing methods for heterophilic graphs often neglect valuable information or are ineffective, leading to poor performance in downstream tasks.
• This highlights a need for advanced GNN architectures capable of handling diverse graph structures.

Purpose of the Study:

• To propose a novel framework, GARN, for effective extraction of both homophilic and heterophilic information from graph data.
• To address the limitations of current GNNs in processing heterophilic graphs.
• To enhance graph representation learning for tasks like node and graph classification.

Main Methods:

• Analysis of GNN shortcomings in heterophilic graph processing using spectral and spatial theories.
• Design of a Graph Aggregating-Repelling Convolution (GARC) mechanism to fuse low-pass and high-pass graph filters.
• Implementation of GARC with positive and negative attention weights for aggregating similar and repelling dissimilar nodes, respectively, controlled by a learnable integration weight.

Main Results:

• The proposed GARN framework, by stacking GARC layers, demonstrates effectiveness in graph representation learning.
• Experiments on homophilic, heterophilic, and image-converted graphs show superior performance compared to existing GNN baselines.
• The GARC mechanism adaptively balances aggregation and repulsion, preventing over-reliance on intra-class similarity.

Conclusions:

• GARN effectively extracts both homophilic and heterophilic information, outperforming baseline GNNs on various graph datasets.
• The GARC mechanism provides a flexible approach to graph filtering, adaptable to different graph properties.
• The framework shows significant potential for improving performance in node and graph classification tasks on complex graph structures.