arXiv Machine Learning
Graph Matching Relaxations and Amortization for Supervised Graph Prediction
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arXiv AI
Jul 9
Diffusion enabled Optimal Transport distances for graph matching
arXiv:2607. 06646v1 Announce Type: cross Abstract: This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport.
arXiv Machine Learning
Jul 28
On a linear fused Gromov-Wasserstein distance for graph structured data
arXiv:2203. 04711v2 Announce Type: replace Abstract: We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem.
arXiv Machine Learning
Aug 31
Optimal Transport for Network Comparison: A Review with Machine Learning Applications
The paper reviews the use of optimal transport for comparing undirected, unweighted graphs, focusing on three main distances: Wasserstein, Gromov-Wasserstein, and Bures-Wasserstein. It discusses closed-form solutions for the Wasserstein distance in one dimension, how transport plans identify influential nodes after perturbations, and derives spectral bounds for the Bures-Wasserstein distance to avoid full decompositions. The authors evaluate these distances on synthetic clustering data and a real-world time‑series network for anomaly detection.
arXiv Machine Learning
Aug 28
Gromov-Monge Flow Matching for Equivariant Graph Generation
The paper introduces Gromov-Monge Flow Matching, a method that incorporates permutation-equivariance into generative graph models by aligning graph pairs up to node relabeling using the Gromov–Monge distance. It shows theoretically that quotient couplings can be lifted to aligned representatives without extra cost and that symmetrization yields equivariant flow-matching minimizers, even for categorical endpoints. Practically, the authors build minibatch couplings with Gromov–Wasserstein relaxations and optional outer assignments, improving sample quality in continuous graph and categorical molecular generation while remaining compatible with standard equivariant architectures.
arXiv Machine Learning
Sep 1
Unsupervised Multi-Scale Gromov-Wasserstein Hypergraph Alignment
arXiv:2608.29635v1 Announce Type: new Abstract: We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information,...
arXiv Machine Learning
3d ago
Optimal Transport for Network Comparison: A Unified Review with New Spectral Bounds and Machine Learning Applications
arXiv:2608.27500v3 Announce Type: replace-cross Abstract: Network comparison using optimal transport is a growing area of research in network science. Unlike standard graph metrics, optimal transport...