157 citations · 242 across the 16 of their papers we have counts for
Showing 2009Show all
2 papers · 1 filter
cs.CG2009★ 2 cited
Quantifying Transversality by Measuring the Robustness of Intersections
Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations,…
math.AT2009★ 22 cited
Persistent Cohomology and Circular Coordinates
Vin de Silva, Mikael Vejdemo-Johansson
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low…