mlsanityData to 7 Oct 2026

A Random Persistence Diagram Generator

arXiv 2104.07737 ↗First posted 15 Apr 2021stat.ML cs.LG math.ATcited by 6

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Abstract (arXiv)

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this paper, we propose a random persistence diagram generator (RPDG) method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned by a model based on pairwise interacting point processes, and a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm. A first example, which is based on a synthetic dataset, demonstrates the efficacy of RPDG and provides a comparison with another method for sampling PDs. A second example demonstrates the utility of RPDG to solve a materials science problem given a real dataset of small sample size.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 9 of its 44 references that are in the map. First posted on arXiv 15 Apr 2021.

Builds on

9 of 44 references.

References · 9

  1. 2013Stochastic Convergence of Persistence Landscapes and Silhouettescited by 43
  2. 2014Robust Topological Inference: Distance To a Measure and Kernel Distancecited by 25
  3. 2013Confidence sets for persistence diagramscited by 17
  4. 2013Hypothesis Testing for Topological Data Analysiscited by 9
  5. 2019Bayesian Topological Learning for Brain State Classificationcited by 7
  6. 2021Topological Deep Learningcited by 6
  7. 2017Modeling and replicating statistical topology, and evidence for CMB non-homogeneitycited by 4
  8. 2013Probabilistic Fr'echet Means for Time Varying Persistence Diagramscited by 3
  9. 2018A Stable Cardinality Distance for Topological Classificationcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 0; 2024: 3; 2025: 0; 2026: 1.

6 papers.

  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2022A Topological Deep Learning Framework for Neural Spike Decodingcited by 6
  3. 2022Quantum Persistent Homology for Time Seriescited by 4
  4. 2024Quantum Distance Approximation for Persistence Diagramscited by 1
  5. 2024Topological Detection of Phenomenological Bifurcations with Unreliable Kernel Densitiescited by 0
  6. 2026Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learningcited by 0