# COPT: Coordinated Optimal Transport for Graph Sketching

arXiv: https://arxiv.org/abs/2003.03892 · HTML: https://mlsanity.com/paper/2003.03892/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 17 of 17)

- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Hierarchical Multi-Marginal Optimal Transport for Network Alignment](https://mlsanity.com/paper/2310.04470/) (2023)
- [Partially Does It: Towards Scene-Level FG-SBIR with Partial Input](https://mlsanity.com/paper/2203.14804/) (2022)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [Joint Optimal Transport and Embedding for Network Alignment](https://mlsanity.com/paper/2502.19334/) (2025)
- [Generalized Sobolev Transport for Probability Measures on a Graph](https://mlsanity.com/paper/2402.04516/) (2024)
- [Computing Approximate Graph Edit Distance via Optimal Transport](https://mlsanity.com/paper/2412.18857/) (2024)
- [GCondenser: Benchmarking Graph Condensation](https://mlsanity.com/paper/2405.14246/) (2024)
- [Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks](https://mlsanity.com/paper/2106.07106/) (2021)
- [UTOPIA: Unconstrained Tracking Objects without Preliminary Examination via Cross-Domain Adaptation](https://mlsanity.com/paper/2306.09613/) (2023)
- [A Quasi-Wasserstein Loss for Learning Graph Neural Networks](https://mlsanity.com/paper/2310.11762/) (2023)
- [Scalable Sobolev IPM for Probability Measures on a Graph](https://mlsanity.com/paper/2502.00737/) (2025)
- [AIGenC: An AI generalisation model via creativity](https://mlsanity.com/paper/2205.09738/) (2022)
- [An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graph](https://mlsanity.com/paper/2502.00739/) (2025)
- [Generalized Sobolev IPM for Graph-Based Measures](https://mlsanity.com/paper/2510.25591/) (2025)
- [Convex Distance Operator Transport: A Convex and Geometry-Preserving Formulation](https://mlsanity.com/paper/2606.02047/) (2026)

## Abstract (arXiv)

We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph representation, applicable to both graph sketching and graph comparison. COPT involves simultaneously optimizing dual transport plans, one between the vertices of two graphs, and another between graph signal probability distributions. We show theoretically that our method preserves important global structural information on graphs, in particular spectral information, and analyze connections to existing studies. Empirically, COPT outperforms state of the art methods in graph classification on both synthetic and real datasets.