# Towards Unsupervised Deep Graph Structure Learning

arXiv: https://arxiv.org/abs/2201.06367 · HTML: https://mlsanity.com/paper/2201.06367/

## Key facts

- Cited by 114 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 60 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 30 of 36)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [DeCLUTR: Deep Contrastive Learning for Unsupervised Textual Representations](https://mlsanity.com/paper/2006.03659/) (2020)
- [InfoXLM: An Information-Theoretic Framework for Cross-Lingual Language Model Pre-Training](https://mlsanity.com/paper/2007.07834/) (2020)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [SLAPS: Self-Supervision Improves Structure Learning for Graph Neural Networks](https://mlsanity.com/paper/2102.05034/) (2021)
- [Self-Supervised Multi-Channel Hypergraph Convolutional Network for Social Recommendation](https://mlsanity.com/paper/2101.06448/) (2021)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)

## Built on by (most cited first, 30 of 114)

- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Federated Learning from Pre-Trained Models: A Contrastive Learning Approach](https://mlsanity.com/paper/2209.10083/) (2022)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Federated Learning on Non-IID Graphs via Structural Knowledge Sharing](https://mlsanity.com/paper/2211.13009/) (2022)
- [Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data](https://mlsanity.com/paper/2306.02664/) (2023)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [Hard Sample Aware Network for Contrastive Deep Graph Clustering](https://mlsanity.com/paper/2212.08665/) (2022)
- [Cluster-guided Contrastive Graph Clustering Network](https://mlsanity.com/paper/2301.01098/) (2023)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection](https://mlsanity.com/paper/2211.04208/) (2022)
- [Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignment](https://mlsanity.com/paper/2502.02017/) (2025)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [GraphEdit: Large Language Models for Graph Structure Learning](https://mlsanity.com/paper/2402.15183/) (2024)
- [OpenGSL: A Comprehensive Benchmark for Graph Structure Learning](https://mlsanity.com/paper/2306.10280/) (2023)
- [Federated Graph Semantic and Structural Learning](https://mlsanity.com/paper/2406.18937/) (2024)
- [A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource](https://mlsanity.com/paper/2211.12875/) (2022)
- [Probabilistically Rewired Message-Passing Neural Networks](https://mlsanity.com/paper/2310.02156/) (2023)
- [Towards Graph Contrastive Learning: A Survey and Beyond](https://mlsanity.com/paper/2405.11868/) (2024)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [CONVERT:Contrastive Graph Clustering with Reliable Augmentation](https://mlsanity.com/paper/2308.08963/) (2023)
- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection](https://mlsanity.com/paper/2307.08390/) (2023)
- [Graph Data Condensation via Self-expressive Graph Structure Reconstruction](https://mlsanity.com/paper/2403.07294/) (2024)
- [Edge Prompt Tuning for Graph Neural Networks](https://mlsanity.com/paper/2503.00750/) (2025)
- [Graph Sparsification via Mixture of Graphs](https://mlsanity.com/paper/2405.14260/) (2024)
- [Reinforcement Graph Clustering with Unknown Cluster Number](https://mlsanity.com/paper/2308.06827/) (2023)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)

## Abstract (arXiv)

In recent years, graph neural networks (GNNs) have emerged as a successful tool in a variety of graph-related applications. However, the performance of GNNs can be deteriorated when noisy connections occur in the original graph structures; besides, the dependence on explicit structures prevents GNNs from being applied to general unstructured scenarios. To address these issues, recently emerged deep graph structure learning (GSL) methods propose to jointly optimize the graph structure along with GNN under the supervision of a node classification task. Nonetheless, these methods focus on a supervised learning scenario, which leads to several problems, i.e., the reliance on labels, the bias of edge distribution, and the limitation on application tasks. In this paper, we propose a more practical GSL paradigm, unsupervised graph structure learning, where the learned graph topology is optimized by data itself without any external guidance (i.e., labels). To solve the unsupervised GSL problem, we propose a novel StrUcture Bootstrapping contrastive LearnIng fraMEwork (SUBLIME for abbreviation) with the aid of self-supervised contrastive learning. Specifically, we generate a learning target from the original data as an "anchor graph", and use a contrastive loss to maximize the agreement between the anchor graph and the learned graph. To provide persistent guidance, we design a novel bootstrapping mechanism that upgrades the anchor graph with learned structures during model learning. We also design a series of graph learners and post-processing schemes to model the structures to learn. Extensive experiments on eight benchmark datasets demonstrate the significant effectiveness of our proposed SUBLIME and high quality of the optimized graphs.