# Gromov-Wasserstein Learning for Graph Matching and Node Embedding

arXiv: https://arxiv.org/abs/1901.06003 · HTML: https://mlsanity.com/paper/1901.06003/

## Key facts

- Cited by 126 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2019.

## Built on by (most cited first, 30 of 126)

- [PLOT: Prompt Learning with Optimal Transport for Vision-Language Models](https://mlsanity.com/paper/2210.01253/) (2022)
- [Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs](https://mlsanity.com/paper/2106.01128/) (2021)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Temporally Consistent Unbalanced Optimal Transport for Unsupervised Action Segmentation](https://mlsanity.com/paper/2404.01518/) (2024)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [OT-Attack: Enhancing Adversarial Transferability of Vision-Language Models via Optimal Transport Optimization](https://mlsanity.com/paper/2312.04403/) (2023)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction](https://mlsanity.com/paper/2202.09025/) (2022)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [Hierarchical Multi-Marginal Optimal Transport for Network Alignment](https://mlsanity.com/paper/2310.04470/) (2023)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [Semi-relaxed Gromov-Wasserstein divergence with applications on graphs](https://mlsanity.com/paper/2110.02753/) (2021)
- [Quantized Gromov-Wasserstein](https://mlsanity.com/paper/2104.02013/) (2021)
- [Fine-Tuning Graph Neural Networks via Graph Topology induced Optimal Transport](https://mlsanity.com/paper/2203.10453/) (2022)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [ZegOT: Zero-shot Segmentation Through Optimal Transport of Text Prompts](https://mlsanity.com/paper/2301.12171/) (2023)
- [A Fused Gromov-Wasserstein Framework for Unsupervised Knowledge Graph Entity Alignment](https://mlsanity.com/paper/2305.06574/) (2023)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2210.06671/) (2022)
- [Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport](https://mlsanity.com/paper/2301.12721/) (2023)
- [Graph Mixup with Soft Alignments](https://mlsanity.com/paper/2306.06788/) (2023)
- [A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarsening](https://mlsanity.com/paper/2306.08854/) (2023)
- [Fused Gromov-Wasserstein Graph Mixup for Graph-level Classifications](https://mlsanity.com/paper/2306.15963/) (2023)
- [Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformers](https://mlsanity.com/paper/2404.09411/) (2024)
- [It's a (Blind) Match! Towards Vision-Language Correspondence without Parallel Data](https://mlsanity.com/paper/2503.24129/) (2025)
- [Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification](https://mlsanity.com/paper/2205.13573/) (2022)
- [A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Data](https://mlsanity.com/paper/2303.06595/) (2023)
- [Joint Self-Supervised Video Alignment and Action Segmentation](https://mlsanity.com/paper/2503.16832/) (2025)
- [Reversible Gromov-Monge Sampler for Simulation-Based Inference](https://mlsanity.com/paper/2109.14090/) (2021)

## Abstract (arXiv)

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node embeddings associated with the two graphs are learned under the guidance of the optimal transport, the distance of which not only reflects the topological structure of each graph but also yields the correspondence across the graphs. These two learning steps are mutually-beneficial, and are unified here by minimizing the Gromov-Wasserstein discrepancy with structural regularizers. This framework leads to an optimization problem that is solved by a proximal point method. We apply the proposed method to matching problems in real-world networks, and demonstrate its superior performance compared to alternative approaches.