A Geometric Perspective on Sparse Filtrations
Computational Geometry
2015-06-12 v1
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.
Cite
@article{arxiv.1506.03797,
title = {A Geometric Perspective on Sparse Filtrations},
author = {Nicholas J. Cavanna and Mahmoodreza Jahanseir and Donald R. Sheehy},
journal= {arXiv preprint arXiv:1506.03797},
year = {2015}
}