# Gromov-Wasserstein Factorization Models for Graph Clustering

arXiv: https://arxiv.org/abs/1911.08530 · HTML: https://mlsanity.com/paper/1911.08530/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2019.

## Built on by (most cited first, 25 of 25)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [Semi-relaxed Gromov-Wasserstein divergence with applications on graphs](https://mlsanity.com/paper/2110.02753/) (2021)
- [Template based Graph Neural Network with Optimal Transport Distances](https://mlsanity.com/paper/2205.15733/) (2022)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [InfiGFusion: Graph-on-Logits Distillation via Efficient Gromov-Wasserstein for Model Fusion](https://mlsanity.com/paper/2505.13893/) (2025)
- [On a linear fused Gromov-Wasserstein distance for graph structured data](https://mlsanity.com/paper/2203.04711/) (2022)
- [Learning Graphon Autoencoders for Generative Graph Modeling](https://mlsanity.com/paper/2105.14244/) (2021)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [Regularized Optimal Transport Layers for Generalized Global Pooling Operations](https://mlsanity.com/paper/2212.06339/) (2022)
- [Fast Gradient Computation for Gromov-Wasserstein Distance](https://mlsanity.com/paper/2404.08970/) (2024)
- [Exploiting Edge Features in Graphs with Fused Network Gromov-Wasserstein Distance](https://mlsanity.com/paper/2309.16604/) (2023)
- [A Quasi-Wasserstein Loss for Learning Graph Neural Networks](https://mlsanity.com/paper/2310.11762/) (2023)
- [When does the mean network capture the topology of a sample of networks?](https://mlsanity.com/paper/2408.03461/) (2024)
- [Transfer Learning on Edge Connecting Probability Estimation under Graphon Model](https://mlsanity.com/paper/2510.05527/) (2025)
- [Revisiting Global Pooling through the Lens of Optimal Transport](https://mlsanity.com/paper/2201.09191/) (2022)
- [Structure-Sensitive Graph Dictionary Embedding for Graph Classification](https://mlsanity.com/paper/2306.10505/) (2023)
- [Interpolating between Clustering and Dimensionality Reduction with Gromov-Wasserstein](https://mlsanity.com/paper/2310.03398/) (2023)
- [Robust Graph Matching Using An Unbalanced Hierarchical Optimal Transport Framework](https://mlsanity.com/paper/2310.12081/) (2023)
- [Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Models](https://mlsanity.com/paper/2605.28488/) (2026)
- [Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms](https://mlsanity.com/paper/2608.11016/) (2026)
- [A dictionary learning framework for graphs via filters and optimal transport](https://mlsanity.com/paper/2609.05919/) (2026)

## Abstract (arXiv)

We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a set of atoms with different weights. By minimizing the GW discrepancy between each observed graph and its GW barycenter-based estimation, we learn the atoms and their weights associated with the observed graphs. The model achieves a novel and flexible factorization mechanism under GW discrepancy, in which both the observed graphs and the learnable atoms can be unaligned and with different sizes. We design an effective approximate algorithm for learning this Gromov-Wasserstein factorization (GWF) model, unrolling loopy computations as stacked modules and computing gradients with backpropagation. The stacked modules can be with two different architectures, which correspond to the proximal point algorithm (PPA) and Bregman alternating direction method of multipliers (BADMM), respectively. Experiments show that our model obtains encouraging results on clustering graphs.