mlsanityData to 7 Oct 2026

Statistical Analysis and Parameter Selection for Mapper

arXiv 1706.00204 ↗First posted 1 Jun 2017cs.CG math.AT stat.MEcited by 20

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Abstract (arXiv)

In this article, we study the question of the statistical convergence of the 1-dimensional Mapper to its continuous analogue, the Reeb graph. We show that the Mapper is an optimal estimator of the Reeb graph, which gives, as a byproduct, a method to automatically tune its parameters and compute confidence regions on its topological features, such as its loops and flares. This allows to circumvent the issue of testing a large grid of parameters and keeping the most stable ones in the brute-force setting, which is widely used in visualization, clustering and feature selection with the Mapper.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jun 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 1; 2023: 3; 2024: 6; 2025: 3; 2026: 4.

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  1. 2023The Disagreement Problem in Faithfulness Metricscited by 6
  2. 2021A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysiscited by 5
  3. 2024Differentiable Mapper For Topological Optimization Of Data Representationcited by 5
  4. 2024MOUNTAINEER: Topology-Driven Visual Analytics for Comparing Local Explanationscited by 4
  5. 2025Explainable Mapper: Charting LLM Embedding Spaces Using Perturbation-Based Explanation and Verification Agentscited by 4
  6. 2021Mapper-type algorithms for complex data and relationscited by 3
  7. 2024AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithmcited by 3
  8. 2023Topological Interpretability for Deep-Learningcited by 2
  9. 2023G-Mapper: Learning a Cover in the Mapper Constructioncited by 2
  10. 2024A distribution-guided Mapper algorithmcited by 2
  11. 2022Topological structure of complex predictionscited by 1
  12. 2024Improving Mapper's Robustness by Varying Resolution According to Lens-Space Densitycited by 1
8 more
  1. 2025Cover Learning for Large-Scale Topology Representationcited by 1
  2. 2025Topological Data Analysis for Unsupervised Anomaly Detection and Customer Segmentation on Banking Datacited by 1
  3. 2021Statistical embedding: Beyond principal componentscited by 0
  4. 2024A Mapper Algorithm with implicit intervals and its optimizationcited by 0
  5. 2026Structure-First Point Cloud Learning with Mapper Region Graphscited by 0
  6. 2026AMD-FCG: An Enhanced Function Call Graph Dataset with Integrated Topological Features for Malware Detection and Classificationcited by 0
  7. 2026Structured Learning on Mapper Representationscited by 0
  8. 2026Skeletal Prototypes on Iterative Nerve Expansionscited by 0