# Unreduced Persistence Diagrams for Topological Machine Learning

arXiv: https://arxiv.org/abs/2507.07156 · HTML: https://mlsanity.com/paper/2507.07156/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 47 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [Clique topology reveals intrinsic geometric structure in neural correlations](https://mlsanity.com/paper/1502.06172/) (2015)
- [Induced Matchings and the Algebraic Stability of Persistence Barcodes](https://mlsanity.com/paper/1311.3681/) (2013)
- [Keeping it sparse: Computing Persistent Homology revisited](https://mlsanity.com/paper/2211.09075/) (2022)
- [DONUT -- Creation, Development, and Opportunities of a Database](https://mlsanity.com/paper/2304.12417/) (2023)

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

- [Foundations of Artificial Intelligence Frameworks: Notion and Limits of AGI](https://mlsanity.com/paper/2511.18517/) (2025)

## Abstract (arXiv)

Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the most computationally demanding step in such a pipeline, however. To explore this dynamic, we introduce several methods to generate topological feature vectors from unreduced boundary matrices and investigate their theoretical and computational properties. We compared the performance of pipelines trained on vectorizations of unreduced PDs to vectorizations of fully-reduced PDs across several data and task types. Our results indicate that models trained on PDs built from unreduced diagrams can perform on par and even outperform those trained on fully-reduced diagrams on some tasks. We also benchmarked the computational performance of an algorithm for computing unreduced diagrams, which was implemented as a heavily modified version of Ripser. These computations are parallelizable and required an order of magnitude less memory on average compared to computing full persistence diagrams. Our results suggest that machine learning pipelines which incorporate topology-based features may benefit in terms of computational cost and performance by utilizing information contained in unreduced boundary matrices.