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.

@inproceedings{cavanna15geometric,
	Author = {Nicholas J. Cavanna and Mahmoodreza Jahanseir and Donald R. Sheehy},
	Booktitle = {Proceedings of the Canadian Conference on Computational Geometry},
	Title = {A Geometric Perspective on Sparse Filtrations},
  Pages = {116--121},
	Year = {2015}}