Addressing Graph Heterogeneity and Heterophily from A Spectral Perspective

TL;DR

This work addresses heterogeneity and heterophily in graphs by introducing a spectral GNN, $H^2$SGNN, built from two complementary modules: local independent filtering and global hybrid filtering. Local filtering processes each meta-path separately to capture diverse homophily levels, while global filtering aggregates meta-paths to explore higher-order neighborhoods with reduced parameter growth. The model achieves competitive or superior performance on four heterogeneous datasets using linear parameter scaling, and provides interpretability through learned, meta-path-specific filters. Theoretical and empirical results demonstrate that the global hybrid filter can emulate multivariate polynomials under certain conditions, enabling rich expressiveness without the exponential cost of prior approaches. The approach offers practical advantages in memory efficiency and scalability, making higher-order meta-path exploration feasible in heterogeneous-heterophilic graphs.

Abstract

Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly hinder the performance of GNNs. Heterogeneity refers to a graph with multiple types of nodes or edges, while heterophily refers to the fact that connected nodes are more likely to have dissimilar attributes or labels. Although there have been few works studying heterogeneous heterophilic graphs, they either only consider the heterophily of specific meta-paths and lack expressiveness, or have high expressiveness but fail to exploit high-order neighbors. In this paper, we propose a Heterogeneous Heterophilic Spectral Graph Neural Network (H2SGNN), which employs two modules: local independent filtering and global hybrid filtering. Local independent filtering adaptively learns node representations under different homophily, while global hybrid filtering exploits high-order neighbors to learn more possible meta-paths. Extensive experiments are conducted on four datasets to validate the effectiveness of the proposed H2SGNN, which achieves superior performance with fewer parameters and memory consumption. The code is available at the GitHub repo: https://github.com/Lukangkang123/H2SGNN/.

Figures (10)

• Figure 1: Example of four types of graphs based on heterogeneity and heterophily. The horizontal axis is heterogeneity, which is divided into homogeneous and heterogeneous graphs from left to right. The vertical axis is heterophily, which is divided into homophilic and heterophilic graphs from bottom to top. "Paper" is the target node to be classified.
• Figure 2: The overall framework of the proposed H$^2$SGNN model, where "paper" is the target node. At first, we obtain different adjacency matrices $\mathbf{A}_i$ according to different meta-paths in the heterogeneous graph, and then use different filter functions $h_i(\lambda)$ to obtain the matrix $h_i(\mathbf{A}_i)$. At the same time, the global filter function $g(\mathbb{A})$ filters the global adjacency matrix. Finally, all filtered matrices are added and multiplied with the feature matrix for the node classification task.
• Figure 3: A simple example of a global hybrid filter exploring more diverse paths, where $\beta_1$ and $\beta_2$ are learnable parameters corresponding to the predefined meta-paths $PAP$ and $PCP$ in Eq. (\ref{['eq:beta']}), respectively. The learned meta-paths include $PAPAP$, $PAPCP$, $PCPAP$, and $PCPCP$ as shown in Eq. (\ref{['eq:more_path']}).
• Figure 4: Ablation study of proposed H$^2$SGNN on four datasets with two variants H$^2$SGNN-$g$ and H$^2$SGNN-$l$.
• Figure 5: Effect of order $K$ on model performance.

Theorems & Definitions (1)

• Proposition 1