HeRB: Heterophily-Resolved Structure Balancer for Graph Neural Networks

TL;DR

HeRB tackles the joint challenge of structural imbalance and heterophily in graphs by first rectifying heterophily through a heterophily-lessening augmentation and then transferring homophilic knowledge from head to tail nodes. The method combines a structure-feature based augmentation, a translation-based neighborhood expansion, and a localizing translation learner, with losses that constrain head-node neighborhoods and optimize supervised objectives. Empirical results across eight datasets show HeRB achieving state-of-the-art performance, particularly on heterophilic graphs, with ablations confirming the contributions of both augmentation and knowledge transfer components. The work advances practical GNN performance by improving tail-node learning and providing theoretical justification via entropy-based analysis of message diversity. Overall, HeRB offers a scalable, effective framework for structure-balancing in heterogeneous graphs with heterogeneous node connectivity patterns.

Abstract

Recent research has witnessed the remarkable progress of Graph Neural Networks (GNNs) in the realm of graph data representation. However, GNNs still encounter the challenge of structural imbalance. Prior solutions to this problem did not take graph heterophily into account, namely that connected nodes process distinct labels or features, thus resulting in a deficiency in effectiveness. Upon verifying the impact of heterophily on solving the structural imbalance problem, we propose to rectify the heterophily first and then transfer homophilic knowledge. To the end, we devise a method named HeRB (Heterophily-Resolved Structure Balancer) for GNNs. HeRB consists of two innovative components: 1) A heterophily-lessening augmentation module which serves to reduce inter-class edges and increase intra-class edges; 2) A homophilic knowledge transfer mechanism to convey homophilic information from head nodes to tail nodes. Experimental results demonstrate that HeRB achieves superior performance on two homophilic and six heterophilic benchmark datasets, and the ablation studies further validate the efficacy of two proposed components.

Figures (5)

• Figure 1: The left figure illustrates the imbalanced distributions of node degrees in the CiteSeer and Chameleon datasets. The right figure presents the Micro-F1 results of GCN on the node classification task, where both head nodes and tail nodes suffer from their heterophily, leading to poorer classification performance.
• Figure 2: The overall framework of HeRB. The framework contains two modules: heterophily-lessening augmentation and homophilic knowledge transfer. The first module corrects the heterophily of the graph by increasing intra-class edges and removing inter-class edges. The second module explores the latent neighbourhood of tail nodes from head nodes and transfer the translation relationship between the expanded neighbourhood and the tail nodes during message passing.
• Figure 3: Performance variation when changing hyper-parameters $T_{hete}$ from 0 to 0.5 (step 0.1) and $T_{homo}$ from 0.5 to 1 (step 0.1), with other parameters fixed.
• Figure 4: Performance variation when changing hyper-parameters $\alpha$ and $\beta$ from 0.05 to 0.95 (step 0.05), with other parameters fixed.
• Figure 5: Performance variation when changing hyper-parameters $k$ from 5 to 20 on Cornell and Texas, 30 on Wisconsin, and 50 on other datasets (step 5) and $\mu$ from 0.001 to 0.01 with (step 0.001), with other parameters fixed.