157 citations · 242 across the 16 of their papers we have counts for
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Parametrized Homology via Zigzag Persistence
Gunnar Carlsson, Vin de Silva, Sara Kalisnik +1
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding…
Dualities in persistent (co)homology
Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their p…
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…