Publications (52)
Convergence of Leray Cosheaves for Decorated Mapper Graphs
Justin Curry, Washington Mio, Tom Needham +2
We introduce decorated mapper graphs as a generalization of mapper graphs capable of capturing more topological information of a data set. A decorated mapper graph can be viewed as…
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…
Optimization and the Topology of Spaces of Parseval Frames
Anthony Caine, Tom Needham, Clayton Shonkwiler
A Parseval frame is a spanning set for a Hilbert space which satisfies the Parseval identity: a vector can be expressed as a linear combination of the frame whose coefficients are…
Quantized Gromov-Wasserstein
Samir Chowdhury, David Miller, Tom Needham
The Gromov-Wasserstein (GW) framework adapts ideas from optimal transport to allow for the comparison of probability distributions defined on different metric spaces. Scalable comp…
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…
Geometric averages of partitioned datasets
Tom Needham, Thomas Weighill
We introduce a method for jointly registering ensembles of partitioned datasets in a way which is both geometrically coherent and partition-aware. Once such a registration has been…