# A distribution-guided Mapper algorithm

arXiv: https://arxiv.org/abs/2401.12237 · HTML: https://mlsanity.com/paper/2401.12237/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 37 references that are in the map.
- First posted on arXiv 19 Jan 2024.

## Builds on (most cited first, 5 of 5)

- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Statistical Analysis and Parameter Selection for Mapper](https://mlsanity.com/paper/1706.00204/) (2017)
- [Confidence sets for persistence diagrams](https://mlsanity.com/paper/1303.7117/) (2013)
- [Structure and Stability of the 1-Dimensional Mapper](https://mlsanity.com/paper/1511.05823/) (2015)
- [Topological Analysis of Nerves, Reeb Spaces, Mappers, and Multiscale Mappers](https://mlsanity.com/paper/1703.07387/) (2017)

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

- [A Mapper Algorithm with implicit intervals and its optimization](https://mlsanity.com/paper/2412.11631/) (2024)
- [Skeletal Prototypes on Iterative Nerve Expansions](https://mlsanity.com/paper/2609.16170/) (2026)

## Abstract (arXiv)

Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This graph is often regarded as an approximation of a reeb graph of data. The classic Mapper algorithm uses fixed interval lengths and overlapping ratios, which might fail to reveal subtle features of data, especially when the underlying structure is complex. Results: In this work, we introduce a distribution guided Mapper algorithm named D-Mapper, that utilizes the property of the probability model and data intrinsic characteristics to generate density guided covers and provides enhanced topological features. Our proposed algorithm is a probabilistic model-based approach, which could serve as an alternative to non-prababilistic ones. Moreover, we introduce a metric accounting for both the quality of overlap clustering and extended persistence homology to measure the performance of Mapper type algorithm. Our numerical experiments indicate that the D-Mapper outperforms the classical Mapper algorithm in various scenarios. We also apply the D-Mapper to a SARS-COV-2 coronavirus RNA sequences dataset to explore the topological structure of different virus variants. The results indicate that the D-Mapper algorithm can reveal both vertical and horizontal evolution processes of the viruses. Availability: Our package is available at https://github.com/ShufeiGe/D-Mapper.