# Fast Topological Signal Identification and Persistent Cohomological Cycle Matching

arXiv: https://arxiv.org/abs/2209.15446 · HTML: https://mlsanity.com/paper/2209.15446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [Induced Matchings and the Algebraic Stability of Persistence Barcodes](https://mlsanity.com/paper/1311.3681/) (2013)
- [Efficient Computation of Image Persistence](https://mlsanity.com/paper/2201.04170/) (2022)
- [Lifespan Functors and Natural Dualities in Persistent Homology](https://mlsanity.com/paper/2012.12881/) (2020)
- [A Coupled Alpha Complex](https://mlsanity.com/paper/2105.08113/) (2021)
- [Persistent Extension and Analogous Bars: Data-Induced Relations Between Persistence Barcodes](https://mlsanity.com/paper/2201.05190/) (2022)

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

- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Cycles Communities from the Perspective of Dendrograms and Gradient Sampling](https://mlsanity.com/paper/2512.12974/) (2025)

## Abstract (arXiv)

Within the context of topological data analysis, the problems of identifying topological significance and matching signals across datasets are important and useful inferential tasks in many applications. The limitation of existing solutions to these problems, however, is computational speed. In this paper, we harness the state-of-the-art for persistent homology computation by studying the problem of determining topological prevalence and cycle matching using a cohomological approach, which increases their feasibility and applicability to a wider variety of applications and contexts. We demonstrate this on a wide range of real-life, large-scale, and complex datasets. We extend existing notions of topological prevalence and cycle matching to include general non-Morse filtrations. This provides the most general and flexible state-of-the-art adaptation of topological signal identification and persistent cycle matching, which performs comparisons of orders of ten for thousands of sampled points in a matter of minutes on standard institutional HPC CPU facilities.