# Robust Graph Structure Learning with the Alignment of Features and Adjacency Matrix

arXiv: https://arxiv.org/abs/2307.02126 · HTML: https://mlsanity.com/paper/2307.02126/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 37 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Learning Theory Can (Sometimes) Explain Generalisation in Graph Neural Networks](https://mlsanity.com/paper/2112.03968/) (2021)
- [TAGNN: Target Attentive Graph Neural Networks for Session-based Recommendation](https://mlsanity.com/paper/2005.02844/) (2020)
- [Grale: Designing Networks for Graph Learning](https://mlsanity.com/paper/2007.12002/) (2020)
- [Transductive Rademacher Complexity and its Applications](https://mlsanity.com/paper/1401.3441/) (2014)
- [Deep Iterative and Adaptive Learning for Graph Neural Networks](https://mlsanity.com/paper/1912.07832/) (2019)
- [A Quest for Structure: Jointly Learning the Graph Structure and Semi-Supervised Classification](https://mlsanity.com/paper/1909.12385/) (2019)
- [Graph-based Hierarchical Relevance Matching Signals for Ad-hoc Retrieval](https://mlsanity.com/paper/2102.11127/) (2021)
- [Minimax Lower Bounds for Realizable Transductive Classification](https://mlsanity.com/paper/1602.03027/) (2016)

## Built on by (most cited first, 2 of 2)

- [Joint Graph Rewiring and Feature Denoising via Spectral Resonance](https://mlsanity.com/paper/2408.07191/) (2024)
- [Boolean Product Graph Neural Networks](https://mlsanity.com/paper/2409.14001/) (2024)

## Abstract (arXiv)

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph structure and corresponding representations. To extend the previous work, this paper proposes a novel regularized GSL approach, particularly with an alignment of feature information and graph information, which is motivated mainly by our derived lower bound of node-level Rademacher complexity for GNNs. Additionally, our proposed approach incorporates sparse dimensional reduction to leverage low-dimensional node features that are relevant to the graph structure. To evaluate the effectiveness of our approach, we conduct experiments on real-world graphs. The results demonstrate that our proposed GSL method outperforms several competitive baselines, especially in scenarios where the graph structures are heavily affected by noise. Overall, our research highlights the importance of integrating feature and graph information alignment in GSL, as inspired by our derived theoretical result, and showcases the superiority of our approach in handling noisy graph structures through comprehensive experiments on real-world datasets.