1 citations · 1 across the 7 of their papers we have counts for
8 papers
Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics
Martin Bauer, Facundo Mémoli, Tom Needham +1
A metric space gives rise to three natural classes of infinite-dimensional metric spaces associated to : -Wasserstein spaces of probability measures on , nonlinear Leb…
A Benamou-Brenier Proximal Splitting Method for Constrained Unbalanced Optimal Transport
Mao Nishino, Martin Bauer, Tom Needham +1
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity…
A Persistent Homology Pipeline for the Analysis of Neural Spike Train Data
Cagatay Ayhan, Audrey N. Nash, Roberto Vincis +3
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and…
Equivalence of Landscape and Erosion Distances for Persistence Diagrams
Cagatay Ayhan, Tom Needham
This paper establishes connections between three of the most prominent metrics used in the analysis of persistence diagrams in topological data analysis: the bottleneck distance, P…
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…