Learning node-level representations of heterophilic graphs is crucial for
various applications, including fraudster detection and protein function
prediction. In such graphs, nodes share structural similarity identified by the
equivalence of their connectivity which is implicitly encoded in the form of
higher-order hierarchical information in the graphs. The contrastive methods
are popular choices for learning the representation of nodes in a graph.
However, existing contrastive methods struggle to capture higher-order graph
structures. To address this limitation, we propose a novel multiview
contrastive learning approach that integrates diffusion filters on graphs. By
incorporating multiple graph views as augmentations, our method captures the
structural equivalence in heterophilic graphs, enabling the discovery of hidden
relationships and similarities not apparent in traditional node
representations. Our approach outperforms baselines on synthetic and real
structural datasets, surpassing the best baseline by $16.06\%$ on Cornell,
$3.27\%$ on Texas, and $8.04\%$ on Wisconsin. Additionally, it consistently
achieves superior performance on proximal tasks, demonstrating its
effectiveness in uncovering structural information and improving downstream
applications.

学习异质图的节点级表示对于欺诈者检测和蛋白质功能预测等各种应用至关重要。为了解决传统节点表示无法捕捉高阶图结构的问题，我们提出了一种新颖的多视图对比学习方法，通过在图上集成扩散滤波器，捕捉异质图中的结构等价性，发现传统节点表示中隐含的关系和相似性。我们的方法在合成和真实结构数据集上优于基准方法，在 Cornell 上比最佳基准方法提高了 16.06%，在 Texas 上提高了 3.27%，在 Wisconsin 上提高了 8.04%。此外，我们的方法在近邻任务上始终表现出卓越的性能，证明了其在揭示结构信息和改进下游应用方面的有效性。

非局部图的多分辨结构视图对比学习

Contrastive Learning for Non-Local Graphs with Multi-Resolution  Structural Views

Convolutional neural networks (CNNs) leverage the great power in
representation learning on regular grid data such as image and video. Recently,
increasing attention has been paid on generalizing CNNs to graph or network
data which is highly irregular. Some focus on graph-level representation
learning while others aim to learn node-level representations. These methods
have been shown to boost the performance of many graph-level tasks such as
graph classification and node-level tasks such as node classification. Most of
these methods have been designed for single-dimensional graphs where a pair of
nodes can only be connected by one type of relation. However, many real-world
graphs have multiple types of relations and they can be naturally modeled as
multi-dimensional graphs with each type of relation as a dimension.
Multi-dimensional graphs bring about richer interactions between dimensions,
which poses tremendous challenges to the graph convolutional neural networks
designed for single-dimensional graphs. In this paper, we study the problem of
graph convolutional networks for multi-dimensional graphs and propose a
multi-dimensional convolutional neural network model mGCN aiming to capture
rich information in learning node-level representations for multi-dimensional
graphs. Comprehensive experiments on real-world multi-dimensional graphs
demonstrate the effectiveness of the proposed framework.

本文研究了面向多维图形的图卷积网络模型 mGCN，旨在捕捉学习多维图形节点级表示中的丰富信息，并在真实世界的多维图形上进行了全面实验，证明了该框架的有效性。