From the 1 of 6 linked papers with an AI index.
6 papers
Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance
Thomas Weighill, Chidinma Williams
The paper introduces a diffusion distance based on Metropolis‑Hastings Markov chains to quantify spatial clustering of a distribution on a graph, and develops a statistical test th…
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…
Lifting coarse homotopies
Thomas Weighill
Coarse geometry, and in particular coarse homotopy theory, has proven to be a powerful tool for approaching problems in geometric group theory and higher index theory. In this pape…