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arXiv Machine Learning

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.

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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.

By James Hyun, Fran\c{c}ois G. Meyer
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arXiv Statistics ML
Sep 4

Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing

The paper presents a new duality formulation for the Gromov‑Wasserstein distance that applies to all finitely supported metric‑measure spaces, with and without entropic regularization. Using this duality, the authors derive sample‑complexity bounds and limit distributions for empirical GW distances, and introduce algorithms with formal convergence guarantees. These results enable a principled, efficient method for testing isomorphism between distributions on graphs with a fixed number of nodes based on samples.

By Gabriel Rioux, Joanna Marks, Riccardo Passeggeri, Ziv Goldfeld
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arXiv Machine Learning
Jun 10

$k$-Nearest Neighbors in Gromov--Wasserstein Space

arXiv:2606. 10295v1 Announce Type: cross Abstract: The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry.

By Kaitlyn Hohmeier, Nicolas Fraiman, Caroline Moosmueller
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arXiv Machine Learning
Sep 4

Geometry-Aware Graph Construction via Adaptive Spectral Bandwidth Control

The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.

By Ecem Bozkurt, Antonio Ortega
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