# A Geometric Perspective on Sparse Filtrations

arXiv: https://arxiv.org/abs/1506.03797 · HTML: https://mlsanity.com/paper/1506.03797/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2015.

## Built on by (most cited first, 2 of 2)

- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Measuring Dataset Diversity from a Geometric Perspective](https://mlsanity.com/paper/2602.09340/) (2026)

## Abstract (arXiv)

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.