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Metric properties of partial and robust Gromov-Wasserstein distances
Jannatul Chhoa, Michael Ivanitskiy, Fushuai Jiang +4
The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct m…
The Z-Gromov-Wasserstein Distance
Martin Bauer, Facundo Mémoli, Tom Needham +1
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 n…
Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance
Ranthony A. Clark, Tom Needham, Thomas Weighill
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the in…
Path constrained unbalanced optimal transport
Martin Bauer, Nicolas Charon, Tom Needham +1
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kin…