Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks
Yumeng Wang, Zengyi Wo, Wenjun Wang, Xingcheng Fu, Minglai Shao
TL;DR
This paper tackles graph representation learning on heterophilic graphs where standard GNNs fail due to local, pairwise propagation. It proposes HPGNN, a framework that integrates clique-complex lifting of graphs with Higher-order Personalized PageRank (HiPPR) and Higher-order Adaptive Spectral Convolution (HiASC) to capture multi-scale, higher-order dependencies. The HiPPR generalizes PPR to higher-order simplices with $\Pi^{p}_{HiPPR} = \alpha (I^p - (1-\alpha) \tilde{A}^p)^{-1}$, enabling robust long-range propagation while suppressing boundary noise, and HiASC aggregates signals via order-specific Laplacians $L_p$ with polynomial filters. Experiments on seven datasets show HPGNN outperforms five of seven SOTA in heterophily settings and remains competitive on homophily graphs. The work advances scalable higher-order graph learning and offers practical robustness to noisy inter-class signals.
Abstract
Graph Neural Networks (GNNs) excel in node classification tasks but often assume homophily, where connected nodes share similar labels. This assumption does not hold in many real-world heterophilic graphs. Existing models for heterophilic graphs primarily rely on pairwise relationships, overlooking multi-scale information from higher-order structures. This leads to suboptimal performance, particularly under noise from conflicting class information across nodes. To address these challenges, we propose HPGNN, a novel model integrating Higher-order Personalized PageRank with Graph Neural Networks. HPGNN introduces an efficient high-order approximation of Personalized PageRank (PPR) to capture long-range and multi-scale node interactions. This approach reduces computational complexity and mitigates noise from surrounding information. By embedding higher-order structural information into convolutional networks, HPGNN effectively models key interactions across diverse graph dimensions. Extensive experiments on benchmark datasets demonstrate HPGNN's effectiveness. The model achieves better performance than five out of seven state-of-the-art methods on heterophilic graphs in downstream tasks while maintaining competitive performance on homophilic graphs. HPGNN's ability to balance multi-scale information and robustness to noise makes it a versatile solution for real-world graph learning challenges. Codes are available at https://github.com/streetcorner/HPGNN.