A Geometric Perspective on Sparse Filtrations
classification
💻 cs.CG
keywords
filtrationsperspectivegeometricsparsealgorithmanalysisapplyingcech
read the original abstract
We present a geometric perspective on sparse filtrations used in topological data analysis. This new perspective leads to much simpler proofs, while also being more general, applying equally to Rips filtrations and Cech filtrations for any convex metric. We also give an algorithm for finding the simplices in such a filtration and prove that the vertex removal can be implemented as a sequence of elementary edge collapses.
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Cited by 1 Pith paper
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It's All About Covers: Persistent Homology of Cover Refinements
Cover refinements enable a near-linear-size approximation to the Vietoris-Rips filtration with unconditional log-3 interleaving that preserves persistent homology.
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