A Novel Robust Integrating Method by High-order Proximity for Self-supervised Attribute Network Embedding

Abstract

Fig. 1: The general framework of RSANE consists of three key components: heterogeneous information integration, joint embedding of structures and attributes, and adaptive outlier resistance. Given an attribute network $\mathcal{G}=(\mathbf{A},\mathbf{X})$ where $\mathbf{A}$ is the adjacency matrix and $\mathbf{X}$ is the attribute matrix, topological and semantic information are extracted by first-order proximity and cosine similarity respectively. The integrated weights $\mathbf{Q}$ sum up the topological and semantic information and multiply it by the high-order proximity. It derives three weights to constrain $\mathbf{H}$ in the embedding space, and $\hat{\mathbf{A}}$ and $\hat{\mathbf{X}}$ in the reconstruction space. Loss $\mathcal{L}_{RSANE}$ is calculated based on the outlier weights $\varphi_i$, and the outlier scores $\phi_i$ will be updated based on $\mathcal{L}_{RSANE}$.

Dependencies

matplotlib==3.8.0
numpy==2.1.3
scikit_learn==1.5.2
torch==2.5.1+cu121
torch_geometric==2.6.1

Dataset

In ./data/, the WebKB,Cora, CiteSeer, Amazon and Twitch datasets are provided, along with the corresponding processed versions for link prediction and outlier detection.

Training

Detailed training results and configs for node classification, link prediction, attribute prediction, outlier detection and network visualization are provided in ./Results.ipynb.

Besides, it is also easy to run ./classification.py directly to perform node classification, as is the case for the other graph learning tasks.

Citation

If you find the code useful for your research, we kindly request to consider citing our work:

@article{wu2025novel,
  title={A novel robust integrating method by high-order proximity for self-supervised attribute network embedding},
  author={Wu, Zelong and Wang, Yidan and Hu, Kaixia and Lin, Guoliang and Xu, Xinwei},
  journal={Expert Systems with Applications},
  volume={266},
  pages={125911},
  year={2025},
  publisher={Elsevier}
}