# G-Mapper: Learning a Cover in the Mapper Construction

arXiv: https://arxiv.org/abs/2309.06634 · HTML: https://mlsanity.com/paper/2309.06634/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 56 references that are in the map.
- First posted on arXiv 12 Sep 2023.

## Builds on (most cited first, 4 of 4)

- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Statistical Analysis and Parameter Selection for Mapper](https://mlsanity.com/paper/1706.00204/) (2017)
- [Hypergraph Co-Optimal Transport: Metric and Categorical Properties](https://mlsanity.com/paper/2112.03904/) (2021)
- [Mapper Interactive: A Scalable, Extendable, and Interactive Toolbox for the Visual Exploration of High-Dimensional Data](https://mlsanity.com/paper/2011.03209/) (2020)

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

- [Learning Tangent Bundles and Characteristic Classes with Autoencoder Atlases](https://mlsanity.com/paper/2602.22873/) (2026)
- [Skeletal Prototypes on Iterative Nerve Expansions](https://mlsanity.com/paper/2609.16170/) (2026)

## Abstract (arXiv)

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a ``nice" Mapper graph. This paper focuses on selecting the cover parameter. We present an algorithm that optimizes the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on G-means clustering which searches for the optimal number of clusters in k-means by iteratively applying the Anderson-Darling test. Our splitting procedure employs a Gaussian mixture model to carefully choose the cover according to the distribution of the given data. Experiments for synthetic and real-world datasets demonstrate that our algorithm generates covers so that the Mapper graphs retain the essence of the datasets, while also running significantly faster than a previous iterative method.