# A Random Persistence Diagram Generator

arXiv: https://arxiv.org/abs/2104.07737 · HTML: https://mlsanity.com/paper/2104.07737/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 15 Apr 2021.

## Builds on (most cited first, 9 of 9)

- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Confidence sets for persistence diagrams](https://mlsanity.com/paper/1303.7117/) (2013)
- [Hypothesis Testing for Topological Data Analysis](https://mlsanity.com/paper/1310.7467/) (2013)
- [Bayesian Topological Learning for Brain State Classification](https://mlsanity.com/paper/1912.08348/) (2019)
- [Topological Deep Learning](https://mlsanity.com/paper/2101.05778/) (2021)
- [Modeling and replicating statistical topology, and evidence for CMB non-homogeneity](https://mlsanity.com/paper/1704.08248/) (2017)
- [Probabilistic Fr'echet Means for Time Varying Persistence Diagrams](https://mlsanity.com/paper/1307.6530/) (2013)
- [A Stable Cardinality Distance for Topological Classification](https://mlsanity.com/paper/1812.01664/) (2018)

## Built on by (most cited first, 6 of 6)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [A Topological Deep Learning Framework for Neural Spike Decoding](https://mlsanity.com/paper/2212.05037/) (2022)
- [Quantum Persistent Homology for Time Series](https://mlsanity.com/paper/2211.04465/) (2022)
- [Quantum Distance Approximation for Persistence Diagrams](https://mlsanity.com/paper/2402.17295/) (2024)
- [Topological Detection of Phenomenological Bifurcations with Unreliable Kernel Densities](https://mlsanity.com/paper/2401.16563/) (2024)
- [Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning](https://mlsanity.com/paper/2608.06276/) (2026)

## 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.