4 citations · 6 across the 14 of their papers we have counts for
23 papers
Real Tree Vineyards have Vines
Michael Hull, Thomas Payne, Thomas Weighill
We show that every vineyard can be decomposed into vines, that is, every path in the space of persistence diagrams can be decomposed into a sequence of paths in $\mat…
Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance
Thomas Weighill, Chidinma Williams
We propose a novel measure of the discrepancy between two probability distributions and on a graph - which we call the diffusion distance - that measures the rate of conver…
Topological optimization with birth and death cochains
Thomas Weighill, Ling Zhou
We introduce the notion of birth and death cochains as generalized versions of birth and death simplices in persistent cohomology. We show that birth and death cochains (unlike bir…
Through the Grapevine: Vineyard Distance as a Measure of Topological Dissimilarity
Alvan Arulandu, Daniel Gottschalk, Thomas Payne +2
We introduce a new measure of distance between datasets, based on vineyards from topological data analysis, which we call the vineyard distance. Vineyard distance measures the exte…
Classification of Firn Data via Topological Features
Sarah Day, Jesse Dimino, Matt Jester +2
In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advanta…
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…