# Dory: Overcoming Barriers to Computing Persistent Homology

arXiv: https://arxiv.org/abs/2103.05608 · HTML: https://mlsanity.com/paper/2103.05608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 16 references that are in the map.
- First posted on arXiv 9 Mar 2021.

## Builds on (most cited first, 4 of 4)

- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes](https://mlsanity.com/paper/2001.02581/) (2020)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)

## Built on by (most cited first, 1 of 1)

- [Tight basis cycle representatives for persistent homology of large data sets](https://mlsanity.com/paper/2206.02925/) (2022)

## Abstract (arXiv)

Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various applications, computational requirements have limited applications to small data sets of a few thousand points. We present Dory, an efficient and scalable algorithm that can compute the persistent homology of large data sets. Dory uses significantly less memory than published algorithms and also provides significant reductions in the computation time compared to most algorithms. It scales to process data sets with millions of points. As an application, we compute the PH of the human genome at high resolution as revealed by a genome-wide Hi-C data set. Results show that the topology of the human genome changes significantly upon treatment with auxin, a molecule that degrades cohesin, corroborating the hypothesis that cohesin plays a crucial role in loop formation in DNA.