# Mapper-type algorithms for complex data and relations

arXiv: https://arxiv.org/abs/2109.00831 · HTML: https://mlsanity.com/paper/2109.00831/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 2 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Statistical Analysis and Parameter Selection for Mapper](https://mlsanity.com/paper/1706.00204/) (2017)
- [Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial](https://mlsanity.com/paper/1912.10086/) (2019)
- [Probabilistic Convergence and Stability of Random Mapper Graphs](https://mlsanity.com/paper/1909.03488/) (2019)
- [Convergence between Categorical Representations of Reeb Space and Mapper](https://mlsanity.com/paper/1512.04108/) (2015)

## Built on by (most cited first, 3 of 3)

- [Big data comparison of quantum invariants](https://mlsanity.com/paper/2503.15810/) (2025)
- [On detection probabilities of link invariants](https://mlsanity.com/paper/2509.05574/) (2025)
- [On knot detection via picture recognition](https://mlsanity.com/paper/2510.06284/) (2025)

## Abstract (arXiv)

Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to Ball Mapper that enable encoding of the structure, internal relations and symmetries of the point cloud. Moreover, the strengths of Mapper and Ball Mapper constructions are combined to create a tool for comparing high dimensional data descriptors of a single dataset. This new hybrid algorithm, Mapper on Ball Mapper, is applicable to high dimensional lens functions. As a proof of concept we include applications to knot and game theory, as well as material science and cancer research.