ArticleScientific reports2023
A universal null-distribution for topological data analysis.
Article in Scientific reports, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
3 citing papers in PubMed.
- Cluster Based Association Measures with Applications.Sankhya. Series B. [Methodological.] · 2025Article
- The role of oscillations in grid cells' toroidal topology.PLoS computational biology · 2025Article
- Cluster Persistence for Weighted Graphs.Entropy (Basel, Switzerland) · 2023Article
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Authors and funding
2 authors.
Funding
Abstract
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams arising from data. Despite much effort and its many successful applications, this is largely an open problem. We present a surprising discovery: normalized properly, persistence diagrams arising from random point-clouds obey a universal probability law. Our statements are based on extensive experimentation on both simulated and real data, covering point-clouds with vastly different geometry, topology, and probability distributions. Our results also include an explicit well-known distribution as a candidate for the universal law. We demonstrate the power of these new discoveries by proposing a new hypothesis testing framework for computing significance values for individual topological features within persistence diagrams, providing a new quantitative way to assess the significance of structure in data.
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Registered trials
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