Clarify Confused Nodes via Separated Learning

TL;DR

The paper tackles the degradation of traditional GNNs on heterophilous graphs by challenging the weight-sharing assumption. It introduces Neighborhood Confusion (NC) as a scalable node-wise metric capturing neighborhood label diversity, and builds Neighborhood Confusion-guided Graph Convolutional Network (NCGCN), a two-channel, end-to-end framework that separates low-NC and high-NC nodes with dedicated transformations and intra-group message passing. NC is computed from pseudo-labels during training to produce NC masks that steer two parallel learning streams, significantly improving accuracy across diverse benchmarks and enabling a plug-in extension to other backbones. The work provides theoretical connections between NC, conditional entropy, and classification error bounds, demonstrates empirical SOTA results on ten datasets, and offers practical insights into node distinguishability and feature fusion preferences, with scalability to large graphs and inductive settings.

Abstract

Graph neural networks (GNNs) have achieved remarkable advances in graph-oriented tasks. However, real-world graphs invariably contain a certain proportion of heterophilous nodes, challenging the homophily assumption of traditional GNNs and hindering their performance. Most existing studies continue to design generic models with shared weights between heterophilous and homophilous nodes. Despite the incorporation of high-order messages or multi-channel architectures, these efforts often fall short. A minority of studies attempt to train different node groups separately but suffer from inappropriate separation metrics and low efficiency. In this paper, we first propose a new metric, termed Neighborhood Confusion (NC), to facilitate a more reliable separation of nodes. We observe that node groups with different levels of NC values exhibit certain differences in intra-group accuracy and visualized embeddings. These pave the way for Neighborhood Confusion-guided Graph Convolutional Network (NCGCN), in which nodes are grouped by their NC values and accept intra-group weight sharing and message passing. Extensive experiments on both homophilous and heterophilous benchmarks demonstrate that our framework can effectively separate nodes and yield significant performance improvement compared to the latest methods. The source code will be available in https://github.com/GISec-Team/NCGNN.

Figures (12)

• Figure 1: Illustration of the paradox arising from the node homophily metric.
• Figure 2: Observational experiment on the Coauthor CS dataset. Nodes are divided into 10 groups based on the NH metric, and the test accuracy of GCN across different node groups varies with NH value and the proportion of high-NC nodes. In the group with the lowest NH value, the abnormally high accuracy benefits from the high proportion of low-NC nodes.
• Figure 3: Visualization of embeddings learned by GCN on Coauthor CS dataset before and after guidance by NC metric. Triangles and dots represent high-NC and low-NC nodes, respectively. Observations: (a) The black triangles representing high-NC nodes are primarily distributed at the edges of clusters and tend to gather at the intersection of the decision boundaries, as indicated by the black dashed lines; (b) The circled clusters, composed of different categories of high-NC nodes, require more complex decision boundaries to be effectively separated. (c) After optimization guided by the NC metric, high-NC nodes are distanced from the decision boundaries and are more evenly distributed within the clusters of their corresponding classes.
• Figure 4: Illustration of NCGCN framework. The complete workflow proceeds as follows: 1) calculate NC values of nodes and generate NC masks, which can divide all nodes into high-NC and low-NC groups; 2) the two groups of nodes are trained with specific transformation weights and dropout rates in parallel. Message passing is constrained intra-group at the second layer. The raw features are adaptively added into the outputs. 3) the pseudo labels are used to update the NC values of all nodes, and then the above two processes are repeated until the model converges.
• Figure 5: Distributions of nodes guided by NH and NC, with dashed lines representing the respective averages. Note that using 1-NH instead of NH facilitates comparison between these two metrics. The hops of NC adhere to the optimal value on NCGCN for each dataset during hyperparameter tuning.

Theorems & Definitions (8)

• Definition 1
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• Proposition 4
• proof