Graph Neural Networks for Graphs with Heterophily: A Survey (2202.07082v3)

Abstract: Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriads of graph analytic tasks and applications. In general, most GNNs depend on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that essentially governs existing heterophilic GNN models, along with a general summary and detailed analysis. Furthermore, we discuss the correlation between graph heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out the potential directions to advance and stimulate more future research and applications on heterophilic graph learning with GNNs.

Graph Neural Networks for Graphs with Heterophily: A Survey

The paper titled "Graph Neural Networks for Graphs with Heterophily: A Survey" presents a structured review of Graph Neural Networks (GNNs) tailored for graphs characterized by heterophily. Heterophily, the scenario where nodes with different labels are more likely to be connected, presents unique challenges in graph learning, as it deviates from the homophily assumption dominant in most existing GNNs. The paper aims to systematically categorize and evaluate existing methodologies to enhance GNN capabilities in handling heterophilic graphs.

The authors propose a taxonomy that is primarily divided into three categories: (1) Non-local Neighbor Extension Methods, (2) GNN Architecture Refinement Methods, and (3) Hybrid Methods. Each category addresses distinct aspects of the heterophilic graph learning problem, using either neighbor set expansion, architectural modification, or a combination of both.

1. Non-local Neighbor Extension Methods:

These methods aim to enhance node representation by integrating high-order neighbors into the aggregation process and identifying potential neighbors through novel metrics. Techniques such as high-order neighbor mixing extend the receptive fields of nodes, while methods for potential neighbor discovery redefine "neighborhood" based on structural or feature-based similarities, thereby addressing the local aggregation limitation inherent in homophilic GNNs.

2. GNN Architecture Refinement Methods:

These methods propose enhancements in how messages are aggregated and updated, adapting standard GNN architectures to better handle heterophilic connections. By weighting the messages differently depending on the similarity of neighbors or deepening the network with inter-layer linkage, these refinements help in maintaining expressive and discriminative representations.

3. Hybrid Methods:

Hybrid approaches combine elements from both neighbor extension and architectural refinement strategies, aiming to exploit the advantages of both methods. These models incorporate diverse neighbor information alongside refined aggregation mechanisms to achieve improved performance across varying heterophilic environments.

Numerical Outcomes and Implications:

The authors do not emphasize specific numerical results but rather focus on the conceptual advancements that each method brings to the domain of heterophilic graphs. The strong claim made by the paper is that the existing body of work on heterophily-focused GNNs opens the door for a more rigorous theoretical understanding of heterophily in graph learning tasks.

Future Directions and Developments:

The paper suggests several avenues for future research, including the need for interpretable, scalable, and theoretically grounded models capable of handling heterophily. Additionally, there is a call to expand heterophilic graph learning research beyond node classification to other tasks, such as link prediction and anomaly detection. The exploration of more diverse real-world applications, including biomedicine and financial networks, represents another promising area for the future.

This survey stands as a foundational reference for researchers aiming to explore novel GNN architectures or to investigate the theoretical underpinnings of heterophily. In doing so, it not only consolidates existing knowledge but also posits vital challenges and opportunities in the broader landscape of graph learning.