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Graph Domain Adaptation via Homophily-Agnostic Reconstructing Structure

Ruiyi Fang, Shuo Wang, Ruizhi Pu, Qiuhao Zeng, Hao Zheng, Ziyan Wang, Jiale Cai, Zhimin Mei, Song Tang, Charles Ling, Boyu Wang

TL;DR

Graph Domain Adaptation under label scarcity is challenged by varying homophily between source and target graphs. The authors propose RSGDA, a homophily-agnostic framework that reconstructs both homophilic and heterophilic graphs, applies adaptive filtering, and aligns latent representations through a dual-path encoder architecture. Theoretical analysis shows that mixed graph filtering and spectral alignment reduce distributional mismatch, yielding a bound on target risk that scales with the structural discrepancy $S(G_S,G_T)$. Empirically, RSGDA achieves state-of-the-art accuracy across five benchmarks, with pronounced gains on heterophilic graphs such as WebKB, validating its robustness to homophily shifts and its practical utility for cross-domain node classification.

Abstract

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. However, existing GDA methods typically assume that both source and target graphs exhibit homophily, leading existing methods to perform poorly when heterophily is present. Furthermore, the lack of labels in the target graph makes it impossible to assess its homophily level beforehand. To address this challenge, we propose a novel homophily-agnostic approach that effectively transfers knowledge between graphs with varying degrees of homophily. Specifically, we adopt a divide-and-conquer strategy that first separately reconstructs highly homophilic and heterophilic variants of both the source and target graphs, and then performs knowledge alignment separately between corresponding graph variants. Extensive experiments conducted on five benchmark datasets demonstrate the superior performance of our approach, particularly highlighting its substantial advantages on heterophilic graphs.

Graph Domain Adaptation via Homophily-Agnostic Reconstructing Structure

TL;DR

Graph Domain Adaptation under label scarcity is challenged by varying homophily between source and target graphs. The authors propose RSGDA, a homophily-agnostic framework that reconstructs both homophilic and heterophilic graphs, applies adaptive filtering, and aligns latent representations through a dual-path encoder architecture. Theoretical analysis shows that mixed graph filtering and spectral alignment reduce distributional mismatch, yielding a bound on target risk that scales with the structural discrepancy . Empirically, RSGDA achieves state-of-the-art accuracy across five benchmarks, with pronounced gains on heterophilic graphs such as WebKB, validating its robustness to homophily shifts and its practical utility for cross-domain node classification.

Abstract

Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. However, existing GDA methods typically assume that both source and target graphs exhibit homophily, leading existing methods to perform poorly when heterophily is present. Furthermore, the lack of labels in the target graph makes it impossible to assess its homophily level beforehand. To address this challenge, we propose a novel homophily-agnostic approach that effectively transfers knowledge between graphs with varying degrees of homophily. Specifically, we adopt a divide-and-conquer strategy that first separately reconstructs highly homophilic and heterophilic variants of both the source and target graphs, and then performs knowledge alignment separately between corresponding graph variants. Extensive experiments conducted on five benchmark datasets demonstrate the superior performance of our approach, particularly highlighting its substantial advantages on heterophilic graphs.
Paper Structure (26 sections, 4 theorems, 44 equations, 6 figures, 5 tables)

This paper contains 26 sections, 4 theorems, 44 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Heterophilic Graph Learning
  4. Graph Domain Adaptation
  5. Methodology
  6. Notation
  7. Structure Reconstruction
  8. Homophilic Graph Construction
  9. Construction Optimization
  10. Heterophilic Graph Construction
  11. Graph Filtering
  12. Homophily-agnostic Alignment Network
  13. Theoretical Analysis of RSGDA
  14. Experiments
  15. Datasets
  16. ...and 11 more sections

Key Result

Theorem 1

By using mixed graph filter for source and target graphs, for all input $z$, we have $|\mathbb{E}_{z\sim P_S^O}[h(z)]-\mathbb{E}_{z\sim P_T^O}[h(z)]| < \epsilon$, where $\epsilon$ denotes a small positive constant that can be made arbitrarily small as the optimization proceeds.

Figures (6)

  • Figure 1: Illustration of the graph domain adaptation task (best viewed in color). Given a labeled source graph (color indicates node label) and an unlabeled target graph, there are no labels for us to judge whether the target graph is homophilic or heterophilic.
  • Figure 2: (a) An overview of our method. RSGDA reconstructs structure to obtain homophilic and heterophilic variant graphs, where the final goal is to minimize the graph distribution shift through separately aligning homophily and heterophily. (b) The blue line represents the graph homophily distribution in five benchmarks. The red and green lines demonstrate that after structural reconstruction, RSGDA can effectively separate reconstructed homophilic and heterophilic variants. Homophily means that similar nodes are prone to connect to each other.
  • Figure 3: This show the changes of homophily ratio in homophilic and heterophilic graphs with different hops. Particularly, the nodes in different hops sharing different neighbors have various homophily ratios.
  • Figure 4: The classification accuracy of RSGDA and its variants on four benchmark datasets.
  • Figure 5: The influence of parameters $\mu_1$ and $\mu_2$ on Airport and WebKB datasets.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Definition 1: Structural Difference
  • Theorem 2: Domain Adaptation Bound for Graph Reconstruction
  • Theorem 3
  • Theorem 4: Domain Adaptation Bound for Graph Reconstruction