# Greedy Matroid Algorithm And Computational Persistent Homology

arXiv: https://arxiv.org/abs/2308.01796 · HTML: https://mlsanity.com/paper/2308.01796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2023.

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

- [Topological Interpretations of GPT-3](https://mlsanity.com/paper/2308.03565/) (2023)

## Abstract (arXiv)

An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a sub-sample to the full space. We develop a greedy matroid algorithm for finding an optimal basis for the image of the induced map, and investigate the relationship between this algorithm and the probability of sampling vectors in the image of the induced map.