22 citations · 22 across the 2 of their papers we have counts for
3 papers
Witnessed k-Distance
Leonidas J. Guibas, Quentin Mérigot, Dmitriy Morozov
Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausd…
Homology and Robustness of Level and Interlevel Sets
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov +1
Given a function $f: \Xspace \to \Rspace$ on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups fr…
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…