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.
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
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.
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:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
arXiv:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.
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.
This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition. The distance under consideration, referred to as Max-D-SW, is an adjustment of the Max-Sliced Wasserstein distance.
arXiv:2606. 29665v1 Announce Type: cross Abstract: This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition.
arXiv:2608. 27774v1 Announce Type: cross Abstract: Efficiently and robustly analyzing shape data is critical across many scientific disciplines.
arXiv:2608. 11016v1 Announce Type: cross Abstract: Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like $k$-means.
arXiv:2405. 15768v2 Announce Type: replace-cross Abstract: In this paper, we address the classification of instances represented by distributions on a vector space rather than single points.
arXiv:2606. 30310v1 Announce Type: cross Abstract: The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections.