# Topological data analysis using persistent discrete homology

arXiv: https://arxiv.org/abs/2506.15020 · HTML: https://mlsanity.com/paper/2506.15020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## Builds on (most cited first, 5 of 5)

- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks](https://mlsanity.com/paper/1906.05795/) (2019)
- [Stability of 2-Parameter Persistent Homology](https://mlsanity.com/paper/2010.09628/) (2020)
- [Persistent Homotopy Groups of Metric Spaces](https://mlsanity.com/paper/1912.12399/) (2019)
- [Faster computations of discrete homology](https://mlsanity.com/paper/2410.09939/) (2024)

## Abstract (arXiv)

We propose persistent discrete homology as a tool for topological data analysis and discuss its advantages over the existing methods. In particular, we provide empirical evidence that persistent discrete homology is more noise-resistant than persistent homology of the Vietoris-Rips complex for data coming from non-metric settings.