Over the last few years, there have been several approaches to building sparser complexes that still give good approximations to the persistent homology. In this video, we have illustrated a geometric perspective on sparse filtrations that leads to simpler proofs, more general theorems, and a more visual explanation. We hope that as these techniques become easier to understand, they will also become easier to use.
Visualizing Sparse Filtrations from Don Sheehy on Vimeo.

@inproceedings{cavanna15visualizing,
	Author = {Nicholas J. Cavanna and Mahmoodreza Jahanseir and Donald R. Sheehy},
	Booktitle = {Proceedings of the 31st International Symposium on Computational Geometry},
	Title = {Visualizing Sparse Filtrations},
  Pages =	{23--25},
	Year = {2015}}