# Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport

arXiv: https://arxiv.org/abs/2301.12721 · HTML: https://mlsanity.com/paper/2301.12721/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 76 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 30 of 34)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Language-agnostic BERT Sentence Embedding](https://mlsanity.com/paper/2007.01852/) (2020)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Predicting multicellular function through multi-layer tissue networks](https://mlsanity.com/paper/1707.04638/) (2017)
- [Cross-lingual Entity Alignment via Joint Attribute-Preserving Embedding](https://mlsanity.com/paper/1708.05045/) (2017)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [A Benchmarking Study of Embedding-based Entity Alignment for Knowledge Graphs](https://mlsanity.com/paper/2003.07743/) (2020)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Multi-view Knowledge Graph Embedding for Entity Alignment](https://mlsanity.com/paper/1906.02390/) (2019)
- [Sliced Gromov-Wasserstein](https://mlsanity.com/paper/1905.10124/) (2019)
- [Learning Generative Models across Incomparable Spaces](https://mlsanity.com/paper/1905.05461/) (2019)
- [Relational Reflection Entity Alignment](https://mlsanity.com/paper/2008.07962/) (2020)
- [Visual Pivoting for (Unsupervised) Entity Alignment](https://mlsanity.com/paper/2009.13603/) (2020)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Generalized Spectral Clustering via Gromov-Wasserstein Learning](https://mlsanity.com/paper/2006.04163/) (2020)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [SelfKG: Self-Supervised Entity Alignment in Knowledge Graphs](https://mlsanity.com/paper/2203.01044/) (2022)
- [LargeEA: Aligning Entities for Large-scale Knowledge Graphs](https://mlsanity.com/paper/2108.05211/) (2021)
- [From Alignment to Assignment: Frustratingly Simple Unsupervised Entity Alignment](https://mlsanity.com/paper/2109.02363/) (2021)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Network Enhancement: a general method to denoise weighted biological networks](https://mlsanity.com/paper/1805.03327/) (2018)
- [Mask-GVAE: Blind Denoising Graphs via Partition](https://mlsanity.com/paper/2102.04228/) (2021)

## Built on by (most cited first, 15 of 15)

- [A Fused Gromov-Wasserstein Framework for Unsupervised Knowledge Graph Entity Alignment](https://mlsanity.com/paper/2305.06574/) (2023)
- [No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasets](https://mlsanity.com/paper/2502.02379/) (2025)
- [A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data](https://mlsanity.com/paper/2303.06595/) (2023)
- [PLANETALIGN: A Comprehensive Python Library for Benchmarking Network Alignment](https://mlsanity.com/paper/2505.21366/) (2025)
- [Outlier-Robust Gromov-Wasserstein for Graph Data](https://mlsanity.com/paper/2302.04610/) (2023)
- [Combating Confirmation Bias: A Unified Pseudo-Labeling Framework for Entity Alignment](https://mlsanity.com/paper/2307.02075/) (2023)
- [CombAlign: Enhancing Model Expressiveness in Unsupervised Graph Alignment](https://mlsanity.com/paper/2406.13216/) (2024)
- [AvAtar: Learning to Align via Active Optimal Transport](https://mlsanity.com/paper/2605.24395/) (2026)
- [Robust Graph Matching Using An Unbalanced Hierarchical Optimal Transport Framework](https://mlsanity.com/paper/2310.12081/) (2023)
- [Graph Similarity Computation via Interpretable Neural Node Alignment](https://mlsanity.com/paper/2412.12185/) (2024)
- [Pairwise Similarity Regularization for Semi-supervised Graph Medical Image Segmentation](https://mlsanity.com/paper/2503.12800/) (2025)
- [Network Alignment](https://mlsanity.com/paper/2504.11367/) (2025)
- [Graph Alignment via Dual-Pass Spectral Encoding and Latent Space Communication](https://mlsanity.com/paper/2509.09597/) (2025)
- [An Industrial Dataset for Scene Acquisitions and Functional Schematics Alignment](https://mlsanity.com/paper/2602.15584/) (2026)
- [Towards Effective and Efficient Graph Alignment without Supervision](https://mlsanity.com/paper/2603.08526/) (2026)

## Abstract (arXiv)

Graph alignment, which aims at identifying corresponding entities across multiple networks, has been widely applied in various domains. As the graphs to be aligned are usually constructed from different sources, the inconsistency issues of structures and features between two graphs are ubiquitous in real-world applications. Most existing methods follow the ``embed-then-cross-compare'' paradigm, which computes node embeddings in each graph and then processes node correspondences based on cross-graph embedding comparison. However, we find these methods are unstable and sub-optimal when structure or feature inconsistency appears. To this end, we propose SLOTAlign, an unsupervised graph alignment framework that jointly performs Structure Learning and Optimal Transport Alignment. We convert graph alignment to an optimal transport problem between two intra-graph matrices without the requirement of cross-graph comparison. We further incorporate multi-view structure learning to enhance graph representation power and reduce the effect of structure and feature inconsistency inherited across graphs. Moreover, an alternating scheme based algorithm has been developed to address the joint optimization problem in SLOTAlign, and the provable convergence result is also established. Finally, we conduct extensive experiments on six unsupervised graph alignment datasets and the DBP15K knowledge graph (KG) alignment benchmark dataset. The proposed SLOTAlign shows superior performance and strongest robustness over seven unsupervised graph alignment methods and five specialized KG alignment methods.