Adversarial Network Embedding with Bootstrapped Representations for Sparse Networks

Abstract

Fig. 1: The overall framework of ANEBR. Firstly, network augmentation is performed for positive sampling to extract and filter useful information from the sparse network. ANEBR augments the adjacency matrix $\mathbf{A}$ by extracting latent high-order information and refining it with the $\alpha$-entmax to produce an augmented adjacency matrix $\tilde{\mathbf{A}}$. Secondly, the bootstrapped embedding representation is robustly derived to avoid negative sampling. The target network uses an encoder $\mathcal{E}\xi$ to iteratively bootstrap embeddings $\tilde{\mathbf{H}}$ from $\tilde{\mathbf{A}}$ as targets, updating parameters online based on $\mathcal{E}\theta$ in the online network to stabilize the process. The online network, in turn, uses $\mathcal{E}\theta$ and $\mathcal{D}\theta$ to learn the embedding $\mathbf{H}$ and the reconstruction $\hat{\mathbf{A}}$. The discriminator $\textit{D}\varphi$ differentiates embeddings from both networks, guiding $\mathcal{E}_\theta$ to generate embeddings $\mathbf{H}$ that closely match $\tilde{\mathbf{H}}$ through adversarial interaction. Thirdly, besides learning rich embedding, end-to-end accurate reconstruction is realized. ANEBR seeks low-rank reconstruction errors, i.e., minimizing the sum of singular values in the reconstruction space by the nuclear norm for accurate reconstruction.

Dependencies

entmax==1.3
matplotlib==3.10.0
networkx==3.4.2
numpy==2.2.2
scikit_learn==1.6.1
scipy==1.15.1
torch==2.5.1+cu124
torch_geometric==2.6.1

Dataset

In ./data/, the Adjnoun,20-Newsgroups, PPI, Wikipedia and BlogCatalog datasets are provided, along with the corresponding processed versions for link prediction.

Training

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

Besides, it is also easy to run ./reconstruction.py directly to perform network reconstruction, 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{wu2025adversarial,
  title={Adversarial network embedding with bootstrapped representations for sparse networks},
  author={Wu, Zelong and Wang, Yidan and Lin, Guoliang and Liu, Junlong},
  journal={Applied Intelligence},
  volume={55},
  number={6},
  pages={498},
  year={2025},
  publisher={Springer}
}