# Partial Matchings Induced by Morphisms between Persistence Modules

arXiv: https://arxiv.org/abs/2107.04519 · HTML: https://mlsanity.com/paper/2107.04519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2021.

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

- [Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds](https://mlsanity.com/paper/2402.15058/) (2024)
- [Topological Quality of Subsets via Persistence Matching Diagrams](https://mlsanity.com/paper/2306.02411/) (2023)

## Abstract (arXiv)

We study how to obtain partial matchings using the block function Mf, induced by a morphism f between persistence modules. Mf is defined algebraically and is linear with respect to direct sums of morphisms. We study some interesting properties of Mf, and provide a way to obtain Mf using matrix operations.