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Related papers: Robust Alignment via Partial Gromov-Wasserstein Di…

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The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing…

Machine Learning · Statistics 2026-05-12 Xiaoyun Gong , Gabriel Rioux , Ziv Goldfeld

The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport…

Machine Learning · Computer Science 2025-11-14 Moritz Piening , Robert Beinert

Fused Gromov-Wasserstein (FGW) distances provide a principled framework for comparing objects by jointly aligning structure and node features. However, existing FGW formulations treat all features uniformly, which limits interpretability…

Machine Learning · Computer Science 2026-05-13 Harlin Lee , Ying Yu , Mingxin Li , Ranthony Clark

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…

Statistics Theory · Mathematics 2023-11-23 Yanjun Han , Philippe Rigollet , George Stepaniants

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets -- tasks ubiquitous in data science and machine learning. Because…

Machine Learning · Computer Science 2025-12-04 Sanjit Dandapanthula , Aleksandr Podkopaev , Shiva Prasad Kasiviswanathan , Aaditya Ramdas , Ziv Goldfeld

Comparing metric measure spaces (i.e. a metric space endowed with aprobability distribution) is at the heart of many machine learning problems. The most popular distance between such metric measure spaces is theGromov-Wasserstein (GW)…

Optimization and Control · Mathematics 2023-01-18 Thibault Séjourné , François-Xavier Vialard , Gabriel Peyré

The Gromov-Wasserstein (GW) distance is frequently used in machine learning to compare distributions across distinct metric spaces. Despite its utility, it remains computationally intensive, especially for large-scale problems. Recently, a…

Machine Learning · Statistics 2024-10-01 Antoine Salmona , Julie Delon , Agnès Desolneux

The Gromov-Wasserstein (GW) distance enables comparing metric measure spaces based solely on their internal structure, making it invariant to isomorphic transformations. This property is particularly useful for comparing datasets that…

Statistics Theory · Mathematics 2024-10-24 Gabriel Rioux , Ziv Goldfeld , Kengo Kato

Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…

Machine Learning · Statistics 2020-06-18 Tam Le , Nhat Ho , Makoto Yamada

The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of…

Machine Learning · Statistics 2025-08-15 Mary Chriselda Antony Oliver , Emmanuel Hartman , Tom Needham

We introduce the supervised Gromov-Wasserstein (sGW) optimal transport, an extension of Gromov-Wasserstein by incorporating potential infinity patterns in the cost tensor. sGW enables the enforcement of application-induced constraints such…

Optimization and Control · Mathematics 2024-01-15 Zixuan Cang , Yaqi Wu , Yanxiang Zhao

In this paper, we study the design and analysis of a class of efficient algorithms for computing the Gromov-Wasserstein (GW) distance tailored to large-scale graph learning tasks. Armed with the Luo-Tseng error bound…

Machine Learning · Computer Science 2022-12-15 Jiajin Li , Jianheng Tang , Lemin Kong , Huikang Liu , Jia Li , Anthony Man-Cho So , Jose Blanchet

Recently, two concepts from optimal transport theory have successfully been brought to the Gromov--Wasserstein (GW) setting. This introduces a linear version of the GW distance and multi-marginal GW transport. The former can reduce the…

Numerical Analysis · Mathematics 2022-11-16 Florian Beier , Robert Beinert

In this paper, we newly formulate and solve the optimal density control problem with Gromov-Wasserstein (GW) terminal cost in discrete-time linear Gaussian systems. Differently from the Wasserstein or Kullback-Leibler distances employed in…

Optimization and Control · Mathematics 2024-05-06 Kohei Morimoto , Kenji Kashima

Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…

Statistics Theory · Mathematics 2026-02-04 Tao Wang , Ziv Goldfeld

Matching a source to a target probability measure is often solved by instantiating a linear optimal transport (OT) problem, parameterized by a ground cost function that quantifies discrepancy between points. When these measures live in the…

Machine Learning · Computer Science 2023-11-27 Othmane Sebbouh , Marco Cuturi , Gabriel Peyré

The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly…

Metric Geometry · Mathematics 2026-03-10 Martin Bauer , Facundo Mémoli , Tom Needham , Mao Nishino

Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions,…

The Gromov-Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures…

Probability · Mathematics 2021-04-19 Antoine Salmona , Julie Delon , Agnès Desolneux

Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…

Machine Learning · Computer Science 2026-05-07 Ling Liang , Lei Yang